John,
It's not really "North Bristol" but I do know of site which you can stay at for 2 months. It's called "Newton Mill" (http://www.campinginbath.co.uk) and is located just off the A4 between Bristol and Bath.
We stayed there for six weeks in 2004. There were a number of other people staying on the site on a "long term" basis. We had a problem with our house move and had to vacate our old property and wait six weeks before we could move into the new one.
There are normal tourist pitches and cheaper long term pitches. We chose to stay on a normal tourist pitch, the designated long term pitches have restrictions on the electic hookup capacity and are not in a very nice location witin the site. We stayed there during the July/August peak season and there wasn't a problem with availability. We even went off on "holiday" to other sites a few times and then came back.
The site itself is quite nice with it's own bar/restuarant. My only negative comment is the space between the pitches, they are very cramped. We were only really sleeping there so it didn't bother us too much.
It may not be in your ideal location, but I can recommend it for long term use. The owners are really helpful and understanding and I'm sure they will be able to help you out.
Mark.
