Some of the issues though for rail, when compared to Air services certainly is seating comfort levels on long journey's as well as price which has been previously mentioned in this thread. With regards coaches well, the nearest comparison is probably Nat Ex as
@zwk500 has said. Megabus is like the Ryanair of the coach industry, where they may offer reduced fares, but their seats are uncomfortable if you are travelling for more than an hour.
Whilst railway competition such as you have with LNER, Grand Central, Lumo, Thameslink, Great Northern and Hull Trains to places in the North from Kings Cross, the issue you have is paths. Also, as has been said on many threads, that competition only really works with travelling from London.
Grand central serving Bournemouth would have to be from London Waterloo, as I cannot see them getting the passenger numbers with travelling to Bournemouth from anywhere else. Not sure if it is still the case, but certainly back in the 1990's when I lived in Bournemouth and anytime since I have travelled since to Bournemouth, any Inter-City/XC trains to/from there have been pretty much empty pass Southampton, unless an event is taking place in Bournemouth. So I am nit sure where Grand Central would get any revenue from in doing services to Bournemouth?
In an ideal world, you would have TOC's running services between cities/towns by the sea to those more inland with say Brighton to Holyhead service, that has gone via Redhill to Reading, then up to Oxford, Coventry, Birmingham International, Birmingham New Street. But you then have the issue of would a service like this with missing out customers in London, have enough revenue to keep going and pay for the leasing costs of the trains that you are using?
So, you would have to have competition really on existing routes out of the main stations from London. As well as the competition at Kings Cross, you also have the competition at Euston between Avanti West Coast, Caledonian Sleeper and LNWR (West Midland Trains). With the exception being Caledonian Sleeper, the slower the service, the cheaper the fares.
At any of the other London main stations such as Waterloo, Marylebone, London Bridge, St Pancras, and Victoria you do not really have competition where TOC's are operating the same routes, other than perhaps London Bridge with Southern, Thameslink and South Eastern.