Bath resident here with DD(16). Yes the city isn't what it was, but it is still a great place to live if you can afford it. There is a lot of anger about LTN's, new residents parking zones, street maintenance and bad planning approvals and/or minimal police force amongst a vocal minority.
The Uni has a great reputation (and excellent employability stats). If we didn't live here, I would be encouraging DD to consider a 4 year degree here.
The city is generally very safe, though there are some issues with County lines. The campus is surrounded by National Trust land (but the campus itself is quite compact). It has great sports facilities (as it is a national development centre for a few sports and a football academy).
I believe the Uni has about 18,000 undergraduates (there is a smaller Bath Spa Uni the other side of the City). Accommodation isn't cheap. They are building a bit more on campus, but there are lots of blocks in and around Bath. After year 1 a lot of students try to group together and live in HMO's. The richer foreign students tend to live along North Parade in the new blocks.
There are regular buses from the city up to campus, but September/October are usually chaotic until people learn how to stagger arriving/departing.
I expect that some might find it dull if they are used to edgier big cities.