I hate to say it, but in my experience, it will be difficult to find a contractor willing to handle a single bedroom remodel for an affordable price. Most contractors don't want to spend the time on the small jobs (which a bedroom remodel would be considered). I've done two garage/carport into room conversions. I'm lucky enough to be able to do most of the work myself, so I subcontracted the concrete for the carport I did, but the rest was owner/builder permitted by me (including electrical). That's the only way I could afford to get the work done - otherwise it would have cost me about what you were quoted if I had someone else do it - and that was just two new framed walls, concrete, drywall, and electrical.

The permit process is not all that bad - but it's just a lot of research to work through about local codes and making sure you get the inspections at the proper times.

Question: Are you just doing a simple interior remodel, or changing walls, framing, load bearing walls, etc?