I grew up within a mile or two of Bristol Uni, but my knowledge of their specific halls is limited (primarily limited to talking about the surrounding area, with which I am very familiar!), and I second cupcake's suggestion of asking on TSR.
However, it is normal practice for students in the UK to live in halls for their first year, and the to move out into a shared house, which is rented in the private sector. It's very rare for people to return to halls for second year, and I'm not aware of any university that has accommodation specifically for final year students.
If you wish, you will be able to find spare rooms in student shared houses - it's common to find that people drop out, fall out, want to move houses, and so they need someone to take their place so that they can move, because even if they move out then they remain liable for the rent. Be prepared to find yourself tied into a contract until June 30th though. If you choose to go down this route, look for houses in the Clifton, Redland and Cotham areas, possibly extending your search to somewhere like Hotwells or into Stoke Bishop. If it says City Centre, then be wary, as that's a term often used to pass off locations in less savoury areas like St. Pauls.