I've seen advice that says: clean, use high adhesion primer, and either melamine paint or alkyd enamel with 2 coats of alkyd polyurethane over it. I painted my bathroom floor a couple of years ago using the alkyd paint and poly over. It lasted fine until my daughter dragged her walking cast all over it, and left a pool of water on the floor for hours. The first scratched down to the primer; the second made the whole area covered by the puddle lift up in one piece. The rest of the floor is fine. Guess success depends partly on who is going to use the bath.