When you say, "I have a place", that sounds like it's an unconditional offer which you've accepted. Is that right? So it's not dependent on exam results?
What has the accommodation office said about your situation? Or are they who you're referring to when you say "I've not had much support on the matter"?
As you're no doubt aware, Bristol is not able to offer accomodation to all incoming students. You would fall into the "non-guaranteed" group, given that you missed the deadline. A second round of applications will open on 19th August. This is targeted at new undergraduate students who had Bristol as their insurance choice or who obtain their place via Clearing.
It seems reasonable to assume that you would be able to apply from this date. However, only the accommodation office can tell you for sure.