I'm probably not the best person to answer this, but I want to give some input so I'll give it my best shot. I had Bath as my firm and I've visited the city several times and attended an open day. You are right about accommodation opening up on the 22nd, be as quick as possible once it does open. It's very likely that you will get some sort of accommodation (dependent on how quick you are on the 22nd, availability, etc.) but do not expect en-suite. If you have any mental or physical conditions, they can prioritise you for allocation so do use the online form if applicable. Check out one of the online campus maps to locate each accommodation building, and how they are relative to the maths and econ departments (Brendon Court seems the closest to the econ building). In my opinion, the majority of accommodation provides ample access to central campus and so its hard to go wrong. I've heard that most halls are sociable (particularly the quads), in regards to shared accommodation, Norwood and eastwood/westwood would be up there too. I have to mention though that I've heard some grim things about eastwood, with many saying its the one place to avoid, so take that as you will.