I'm renting to own, my bathroom is cinderblock with a drywall interior. It always has a damp ceiling, which is tongue and groove board, and mold on the drywall. Is there anything I can do to fix this without gutting the walls?

The problem with most condensation issues is warm, moist air wants to move toward cold (to give up its energy) If there is inadequate insulation between the outside and the drywall, all that block is going to be and stay cold, promoting condenstaion. It could also be if this bathroom is below grade, that the block is not properly sealed against moisture from the earth, runoof from the roof, too many shrubs around the foundation, etc. You'd be surprised how little water there needs to be for moisture problems to develop rapidly. Especially if the area is on the shady side of the house.

Before you gut the bathroom, try installing a very good and slightly oversized exhaust fan that you run religiously when you are in the shower and afterwards for a half hour or so. Don't get a cheap fan and be sure if moves plenty of CFM. A room change in a few minutes is great. You need lots of air movement, dry air, and light to keep away mold and mildew. I'd try this first if the moisture is coming from within the house.

If it is coming from the outside you can improve drainage by grading, fixing gutters if you don't get massive ice problems (a sign of poor insulation in the ceiling/roof) removing planting that may be right against the house, putting in drain tile along the perimeter.

Good luck