A mold-resistant, water-based primer, is the best option for priming over bathroom mold and mildew. The only time I would recommend using oil-based primer, like Zinsser Cover Stain, is for only spot priming water and hairspray stains on drywall, but don’t use oil primer across your moldy walls.
A product called "Killz" is an anti mold paint. Might try spraying the area down with a bleach/water mixture (I believe the ratio of 1 part bleach to 10 parts water is sufficient). Spray it down and let it dry. The bleach should kill the mold off in a few days.