We primed our bathroom with an exterior primer and proceeded to paint with the same make of exterior paint. When the shower was used, steam built up in the room. The walls now have water streaks that contain oil. If wiped away with a cloth the next time the shower is used the streak of oil come back.
Applying exterior paint to a bath room is a common idea. However, exterior paints are designed as much for the potential abuse of hot/cold cycles as well as moisture. Exterior finishes should not be used interior.
Now to answer the problem. What should take care of the situation would be to make a trip to the local paint store and purchase a high quality interior oil (not a stain killer) primer. Be sure to ask that it be a universal primer so you will be able to apply a latex finish. Some sheen i.e. eggshell or low-sheen is usually preferable in bath rooms.