You'll be fine, there is plenty to do in Bath and provided you're a little proactive you'll always have something to do i.e.
Night out wise:There's always a decent club to go to in town on a Monday (student) night, and they're generally pretty good on sat and fri too. The union club (Elements) does stuff on Wed, Fri and Sat nights which are usually pretty good. (although I'm informed Friday night tailed off dramatically this year - being on placement for this year I didn't experience it). The uni organises a coach to Bristol every Thursday which costs about £8 return and usually includes either entry or discounted entry into the big clubs in Bristol, trains and buses to Bristol are easy too if you fancy it on a different night.
Clubs, Sports and Societies:So you might have notice Bath is big on sports! facilities and people to play with are usually pretty abundant. There are always loads of things to get involved in. If you find you're getting bored just join a new society - learn to kayak, play tennis, start karate or something. The union has most of the kit to loan out so it wont even cost you. Plus all of the clubs have regular socials and nothing's stopping you from just joining as a social member either in fact some clubs like snow sports encourage it.
In Town:Like the person above mentioned there are plenty of restaurants etc. in Bath and I'm told that it has the highest pub to person ratio in the country! There's a cinema, theatre and nice new shopping complex they are also looking to reopen the quasar in town for next year too. Plus being a world heritage city plenty of museums and national trust sites to look around. Bristol also has plenty to do and get's some good bands and shows and like I said before trains and buses makes it easy to get to.
I've never regretted going to Bath, It's a really nice place to live and I've never been short of things to do! It's a also a quality uni and the placement scheme is second to none (I'd defo recommend doing a placement if you can). The only thing I can say against Bath is it's nowhere near the sea (I come from Poole/Bournemouth Area which has some of the best beaches in the country) but you wont get that in bham either!
Hope that helps and feel free to ask me any further questions - also check out the
Bath SU Web Site for a list of all the clubs etc.
Cheers
Jon