We're so pleased you are both considering Bath! What courses are you thinking about? Apologies for the late reply - as a recent Bath graduate I thought I could jump in here and help out.
When I was looking around at universities I had a similar worry, but for a relative small city and campus compared to places such as Durham or Glasgow, I would say the social life is actually not bad, and there's a surprising amount to do in Bath!
In terms of the uni there are over 150 different societies - arts ones (e.g. musicals, dance, animation/photography, film), sports ones, cultural and course-related ones, and some really quirky ones! (Cheese Society, Skateboarding, Ducks?!). There is also a on-campus nightclub which hosts themed student nights on a Wednesday and a Saturday, the SU puts on events and drop in sessions every week (indoor football & frisbee, free art workshops, dance tasters, salon sessions, pub quizzes), and there's a huge selection of sports facilities and classes which are mostly free to book for students (tennis, badminton, squash courts etc).
In the city there is a healthy choice of nightclubs with theme nights every week, a nice selection of shopping options on Southgate street (4 supermarkets, coffee & street food places, clothes & cosmetic shops such as Lush) and loads of green spaces and cultural spots to visit (more here!) Plus, as Bristol is only 40 mins away on the bus, if you wanted to see a larger city with a little more going on then you can get a student return ticket for £4. You can essentially have the best of both worlds
I hope that helps you both - very best of luck in your next steps and feel free to post any follow-up Qs!