You need to clean the stain first. Warm water, TSP( the cleaning product) bleach, and a drop of dish soap. Clean the stain then let it dry. If the stain is still there, I'd use a shellac based product like Bin. Otherwise it will bleed thru. I think the tsp will take care of your stain though. If the ceiling is in good shape, just pay the extra money and get a gallon of semi gloss paint from Sherwin Williams ( go with the Emerald line) They dont really make a bathroom paint like Ben Moore. They just recommend a higher sheen. I'd go with a primer, but it sounds like you dont want that. I'm a bit of a paint snob, but if you're going to cut corners, do yourself a favor and get a good quality paint.
If you dont want to use the fan, you need to dry that bathroom out as well as you can or youre always going to have mold. Especially in the winter. That's probably where/when it's showing up. If you can, after your shower crank the heat, and shut the door. The ceiling is staying constantly damp otherwise.