My husband and I are here on his work permit for a year, and he is working in Warminster! We looked at flats in Bath when we first went searching, but a few things put us off that you should think about. Bath is an AMAZING city, and I often hop the train to go there for the day, but living there is a bit different. Mainly, the traffic is really really horrible...I would say your fiance would have
at least an hour drive to Warminster from there during traffic times! Add to that the annoyances of finding a parking spot....not fun!

After realizing that and seeing what you can get for the $ in terms of space to $ ratio, we decided to look at other towns on the way to Warminster, but close to Bath.
We are living in Bradford on Avon, about 30min. drive for DH to get to Warminster. It is a really cute stone village. Trowbridge is a bigger town nearby and closer to Warminster, but not much character, good to go to for a Tesco, but kinda run down in our opinion. Higher cost of flats starts to get cheaper there, but it's not the most ideal place to live.
*just realized you said you won't have a car, so nevermind the traffic comments =) In that case, the train station is a good size and easy to use in Bath!

PM me if you have any specific questions about this area!! It'd be fun to meet up with you once you get here, too!