Here is my idea, now this is contigent on plans on other parts of the network and some infrastructure improvements to enable it. It is more for the West of England Metro area than specifically Bristol.
Intercity London Services
London Paddington - Old Oak Common - Reading - Swindon - Chippenham - Bath Spa - Bristol Temple Meads - Weston-super-Mare. 1tph, GWR, 9 Car Class 800/802.
Increased from every 2 hours to every hour, to give a regular nonstop service to/from Weston-super-Mare.
London Paddington - Old Oak Common - Reading - Didcot Parkway - Swindon - Chippenham - Bath Spa - Bristol Temple Meads. 1tph, GWR, 9 Car Class 800/802.
Current service, as is, no changes.
London Paddington - Old Oak Common - Swindon - Bristol Parkway, Split 1 Bristol Temple Meads, Split 2 Newport - Cardiff Central. 2tph, GWR, 2 x 5 Car Class 800/802.
A reintroduction of the super fast services from London, but splitting at Bristol Parkway to save paths to/from London.
London Paddington - Old Oak Common - Reading - Swindon - Bristol Parkway - Newport - Cardiff Parkway - Cardiff Central - Bridgend - Port Talbot Parkway - Neath - Swansea. 1tph, GWR, 9 Car Class 800/802.
Current service, as is, no changes.
London Paddington - Old Oak Common - Reading - Swindon - Bristol Parkway - Newport - Cardiff Parkway - Cardiff Central - Bridgend - Port Talbot Parkway - Neath - Llanelli - Carmarthen. 1tph, GWR, 9 Car Class 800/802.
The current Cardiff terminating service but extended to Carmarthern, this is instead of the new Lumo service, this would better serve South Wales and give better links to/from West Wales.
London Paddington - Old Oak Common - Reading - Swindon - Kemble - Chalfield - Stroud - Stonehouse - Gloucester - Rose-on-Wye - Hereford. 1tph, GWR, 5 Car Class 800/802.
The current service but after Gloucester instead of continuing to Cheltenham Spa, it would continue via the line through Ross-on-Wye to Hereford. (This is a proposed reopening)
London Paddington - Old Oak Common - Reading - Swindon - Kemble - Chalfield - Stroud - Stonehouse - Cheltenham Spa. 1tph, GWR, 5 Car Class 800/802.
An additional service, giving stations along the Golden Valley line 2 services per hour, continuing to Cheltenham Spa.
London Paddington - Old Oak Common - Reading - Newbury - Westbury - Castle Cary (Every other train) - Taunton - Tiverton Parkway - Exeter St Davids - Dawlish - Newton Abbot - Totnes - Ivybridge (Every other train) - Plymouth, Extension 2hrly Liskerd - Bodmin Parkway - Par -Truro - St Erth - Penzance. 1tph, GWR, 9 Car Class 800/802.
The current service, with more reqular extensions to/from Penzance.
London Paddington - Old Oak Common - Reading - Newbury - Westbury - Frome (Every other train) - Taunton - Tiverton Parkway - Exeter St Davids - Dawlish - Newton Abbot - Torre - Torquay - Paignton. 1tph, GWR, 9 Car Class 800/802.
A faster service than the current 2hrly Exeter service and extended to serve Torbay.
Other
Heathrow Express services would become part of the Elizabeth Line, to free up space on the fast lines for more intercity services as once Old Oak Common opens then it will reduce times to/from Heathrow.
Intercity CrossCountry Services
Manchester Piccadilly - Stockport - Macclesfield - Stoke-on-Trent - Stafford - Wolverhampton - Birmingham New Street - Worcestershire Parkway - Cheltenham Spa - Bristol Parkway - Bristol Temple Meads - Taunton - Tiverton Parkway - Exeter St David's, Extension 2hrly Dawlish - Newton Abbot - Torquay - Paignton. 1tph, XC, 7 Car Class 8XX.
The current Manchester to Bristol service, extended to Exeter with 2 hourly extensions to Paignton, Paignton sees a lot of demand from Bristol. Also some higher capacity rolling stock for XC. (It has been proposed before to extend the service down to Exeter anyway)
Newcastle - Durham - Darlington - York - Doncaster - Derby - Burton-on-Trent - Birmingham New Street - Worcestershire Parkway - Cheltenham Spa - Bristol Parkway - Bristol Temple Meads - Taunton - Tiverton Parkway - Exeter St David's, Extension 2hrly Dawlish - Newton Abbot - Totnes - Ivybridge - Plymouth. 1tph, XC, 7 Car Class 8XX.
The current service, but focusing on the core of the route, as customers can change at Exeter for services to all of the South West and higher capacity rolling stock too.
Nottingham - Derby - Burton-on-Trent - Tamworth - Birmingham New Street - Worcestershire Parkway - Cheltenham Spa - Gloucester - Newport - Cardiff Parkway - Cardiff Central. 1tph, XC, 7 Car Class 8XX.
The current service, but sped up by removing stops, and new higher capacity rolling stock.
Leeds - Wakefield Westagte - Sheffield - Chesterfield - Derby - Burton-on-Trent - Brimingham New Street - Worcestershire Parkway - Cheltenham Spa - Gloucester - Newport - Cardiff Parkway - Cardiff Central. 1tph, XC, 7 Car Class 8XX.
The proposed additional hourly service between Birmingham and Cardiff, with an additional hourly service between Leeds and Birmingham.
Semi-fast/Regional Services
London Paddington - Old Oak Common - Slough - Maidenhead - Twyford - Reading - Tilehurst - Pangborune - Goring & Streatley - Chosley - Didcot Parkway - Wantage & Gove - Swindon. 1tph, GWR, 4 Car Class 387.
One of the current half hourly London Paddington to Didcot Parkway services, extended to Swindon via a new station at Wantage & Gove.
London Paddington - Old Oak Common - Slough - Reading - Reading West - Theale - Thatcham - Newbury - Knitbury - Hungerford - Bedwyn - Pewsey - Devizes Gateway - Westbury. 1tph, GWR, 4 Car Class 387.
The current London Paddington to Newbury service, combined with the Newbury to Bedwyn service and extended to Westbury. It would be handy to extend electrification to Westbury as it would allow BEMU's on the other services via Westbury to recharge whilst in the area.
Cardiff Central - Cardiff Parkway - Newport - Filton Abbey Wood - Bristol Temple Meads - Bath Spa - Bradford-on-Avon - Trowbridge - Westbury - Warminster - Wilton Parkway - Salisbury - Romsey - Southampton Central. 1tph, GWR, 5 Car ClassXXX.
As the current service but stopped at Southampton Central, as better connections can be provided from there, with an EMU express service from Southampton to Portsmouth.
Cardiff Central - Cardiff Parkway - Newport - Filton Abbey Wood - Bristol Temple Meads - Weston-super-Mare - Highbridge & Burnham - Bridgwater - Taunton - Wellington - Tiverton Parkway - Cullompton - Exeter St David's. 1tph, GWR, 5 Car ClassXXX.
As the current service but with a more clockface timetable than currently, with stops removed to speed up the service, and local stops moved onto stopping services.
Worcester Foregate Street - Worcester Shrub Hill - Ashchurch for Tewkesbury - Cheltenham Spa - Cam & Dursley - Bristol Parkway - Filton Abbey Wood - Bristol Temple Meads - Bath Spa - Bradford-on-Avon - Trowbridge - Westbury - Warminster - Wilton Parkway - Salisbury - Romsey - Southampton Central. 1tph, GWR, 5 Car ClassXXX.
The current service between Worcester and Bristol but with stops removed to make this service semi-fast, intermediate stops moved to other services, also providing a 2nd semi-fast service between Bristol and Southampton, to connect with a new fast service to/from Brighton.
Birmingham Moor Street - Kings Norton - Bromsgrove - Droitwich Spa - Worcester Shrub Hill - Ashchurch for Tewkesbury - Cheltenham Spa - Gloucester. 1tph, WMR, 2 Car Class 172/196.
The proposed new service from Birmingham Moor Street via the new chords but routed to Gloucester.
Stratford-upon-Avon Parkway - Stratford-upon-Avon - Honeybourne - Cheltenham Racecourse - Cheltenham Spa - Cam & Dursley - Bristol Parkway - Filton Abbey Wood - Bristol Temple Meads - Weston-super-Mare - Highbridge & Burnham - Bridgwater - Taunton - Wellington - Tiverton Parkway - Cullompton - Exeter St David's. 1tph, GWR, 5 Car ClassXXX.
Bristol Temple Meads - Bath Spa - Bradford-on-Avon - Trowbridge - Westbury - Frome - Bruton - Castle Cary - Yeovil Pen Mill - Thornford - Yetminster - Chetnole - Maiden Newton - Dorchester West - Upwey - Weymouth. 1tph, GWR, 5 Car ClassXXX.
The current service, but speeded up with local calls in and around Bristol and Bath removed and frequency improved to finally provide an hourly service.
Bristol Temple Meads - Bath Spa - Chippenham - Swindon - Wantage & Gove - Oxford. 1tph, GWR, 4 Car Class 387.
As the "new" service to be "re"introduced soon but extend electrification from Chippenham down to Bristol Temple Meads and from Didcot Parkway to Oxford so EMU's can be used.
Stopping/Metro Services
Cardiff Central - Cardiff East - Cardiff Parkway - Newport West - Newport - Somerton - Llanwern - Magor & Undy - Severn Tunnel Junction - Pilning - Patchway - Filton Abbey Wood - Lockleaze - Ashley Down - Stapleton Road - Lawrence Hill - Bristol Temple Meads. 2tph, Transport for Wales, 3 Car Class 197.
This would take over stops at Pilning (Have a further idea for how this would be served) and Patchway to allow speeded up GWR services from Cardiff to Bristol (See Below)
Cardiff Central - Cardiff East - Cardiff Parkway - Newport West - Newport - Somerton - Llanwern - Magor & Undy - Severn Tunnel Junction - Caldicot - Chepstow - Lydney - Westbury-on-Severn - Gloucester - Cheltenham Spa. 2tph, Transport for Wales, 2 Car Class 197.
The current service, increased to 2tph as planned.
Gloucester - Cam & Dursley - Charfield - Yate - Bristol Parkway - Filton Abbey Wood - Lockleaze - Ashley Down - Stapleton Road - Lawrence Hill - Bristol Temple Meads. 2tph, GWR, 3 Car ClassXXX.
Effectively a metro service between Bristol and Gloucester. There isn't a need for additional services between Gloucester and Cheltenham Spa. With other planned services, and changes can be made at Bristol Parkway or Cheltenham Spa.
Weston-super-Mare - Weston Milton - Worle - Yatton - Nailsea & Backwell - Long Ashton - Parson Street - Bedminster - Bristol Temple Meads - Lawrence Hill - Stapleton Road - Montpelier - Redland - Clifton Down - Sea Mills - Shirehampton - Portway Park & Ride - Avonmouth Extension hrly St Andrews Road - Severn Beach. 2tph, GWR, 3 Car Class XXX.
The current service between Weston-super-Mare and Avonmouth, with the Bristol Temple Meads to Severn Beach service extended to Weston-super-Mare.
Portishead - Portbury - Pill - Ashton Gate - Parson Street - Bedminster - Bristol Temple Meads - Lawrence Hill - Stapleton Road - Ashley Down - Lockleaze - Filton Abbey Wood - Bristol Brabazon - Henbury. 1tph, GWR, 3 Car ClassXXX.
The current Bristol Temple Meads to Filton Abbey Wood service, as it is proposed to extend it to Henbury and Portishead respectively once the stations are opened.
Portishead - Portbury - Pill - Ashton Gate - Parson Street - Bedminster - Bristol Temple Meads - St Annes Park - Keynsham - Saltford - Oldfield Park - Bath Spa - Corsham - Chippenham - Royal Wotton Bassett - Swindon. 1tph, GWR, 3 Car ClassXXX.
A second train per hour to/from Portishead to Swindon, via a new station at Corsham.
Severn Beach - Henbury - Bristol Brabazon - Filton Abbey Wood - Lockleaze - Ashley Down - Stapleton Road - Lawrence Hill - Bristol Temple Meads - St Annes Park - Keynsham - Saltford - Oldfield Park - Bath Spa - Freshford - Avoncliff - Bradford-on-Avon - Trowbridge - Westbury. 1tph, GWR, 3 Car ClassXXX.
A new service from Severn Beach via the Henbury loop, Bristol Temple Meads and onwards to Westbury, to provide better links to the new arena.
Swindon - Royal Wootton Bassett - Chippenham - Melksham - Trowbridge - Westbury - Frome - Bruton - Castle Cary - Somerton - Taunton. 1tph, GWR, 3 Car ClassXXX.
The proposed Goop! service, that would give Somerton a service and a good Trans Wilts service.
Swindon - Royal Wootton Bassett - Chippenham - Melksham - Trowbridge - Westbury - Dilton Marsh - Warminster - Wilton Parkway - Salisbury. 1tph, GWR, 3 Car ClassXXX.
A more frequent TransWilts service.