As a student who's just finished their second year at Bath, I'd recommend it
I don't know a huge amount about Exeter, so I'll just give you some key points about Bath.
Bath has a placement year option as well as a good reputation with employers of placement students, as well as a lot of support available for interviews, applications etc. Whether you want to do one as well as a masters is your choice - you might find that you want to switch to a BSc anyway, but
you can switch courses after the first year anyway, and the placement year is supposedly invaluable - I guess I'll find out but I can see that
I lived in Eastwood, the cheapest accommodation and it was fine to be honest. It really doesn't matter which is the best socially, anything apart from the accommodation in the city rather than on campus and the designated quiet accommodation and you'll be fine. If you're the type, you'll have those initial freshers week introductions (where you get introduced to and party with your neighborus if you wish) and then it's pretty much up to you and whatever connections you have to party wherever you want.
Uni is pretty good, the campus itself is lovely and has a shop, post office, few eateries and bars, a lake that people sit by when it's warm enough. Level of sport here is pretty high, but there's something for everyone.
Course is alright. Not all of it is interesting or fun but that's to be expected. A lot of interesting options in the third year in particular.