they will be working nightshifts
What exactly will their working pattern be? Nights only or a mixture? Weekdays only or a mixture? What times will they be going to/from work in each case? Are they eligible for any railcard apart from the Network Railcard?
Some points to consider:
* From West Hampstead Thameslink, it's a 3-min walk to West Hampstead Underground, then 15min on the Jubilee Line to Waterloo. This is likely faster (but perhaps less comfortable) than staying on the train to Blackfriars (19min) and walking (15min), or to London Bridge (25min) and changing (5min), even in comparison with trains that are non-stop between St Albans City and St Pancras (which save 1min by skipping West Hampstead). Depending on ticketing it might be more expensive though.
* Although Thameslink trains typically run through the night at Blackfriars, there is a period (roughly 00:30-05:30) when there are no trains at Waterloo East (and no tube, except on weekends).
* An Annual Season Ticket also gives you the Gold Card discount on your Oyster card, i.e. 1/3 discount on off-peak Pay-As-You-Go fares. Thus, paying separately for train or tube from London Bridge will be £2.80 peak (tapping in between 06:30-09:30 or 16:00-19:00) and £1.75 off-peak, and from West Hampstead £3.40 peak and £1.80 off-peak. (The bus price remains at £1.75.) Depending on how often you want to avoid walking from Blackfriars, this could work out cheaper than the £1072 extra for a Travelcard.
* If you can consistently avoid the morning peak (weekdays 04:30 to around 09:30 depending on ticket, or before 10:00 if using Network Railcard), then Railcard-discounted Off-Peak Day Returns might be cheaper than a Season Ticket (which at £4184 or £5256 for the Travelcard makes £16.10/day or £20.22/day if you use it every single weekday for the whole year). However, you'd need to return the same day (i.e. before 04:30 the next morning), or alternatively chain together consecutive night shifts using reverse direction returns (travel home in the late morning on an outward portion, travel to work the same evening on the return portion) but paying a bit more for a period return to get you to work the first evening and back from work the last morning. Further, on weekdays a minimum fare of £13.00 applies with the Network Railcard (meaning you pay £13.00 if the discounted price is lower), or £12.00 if travelling before 10:00 with the 26-30 Railcard. You can avoid the minimum fare by getting the cheapest possible Gold Card Annual Season instead (possibly Hatton to Lapworth at £196.00) and using it solely as a discount card, valid from 09:30 on weekdays.
With the discount, an Off-Peak Day Return from St Albans City to London Thameslink (e.g. Blackfriars or London Bridge) costs £12.00 (not valid morning peak), and a Super Off-Peak Day Return costs £10.00 (not valid morning peak or returning evening peak) or £6.95 (weekends only).
If not walking from Blackfriars, then the Off-Peak Day Return from St Albans City to London Underground Zone 1-2 for £13.45 (not valid morning peak or returning evening peak) allows going to Waterloo East or using the Jubilee Line from West Hampstead or London Bridge, so is cheaper than using PAYG separately. I suspect you can undercut this fare with an Off-Peak Day Return from St Albans City to Queenstown Road (Battersea) route ✠Any Permitted for £12.10 and stopping short at Waterloo, but curiously I can only get Trainsplit to validate taking the train from London Bridge to Waterloo East or the tube from Blackfriars to Waterloo - not tube from London Bridge or West Hampstead to Waterloo, but I see no reason why these routes would not be valid.