When you are choosing a type of paint for the bathroom, I’d recommend a good 100% acrylic interior paint with a satin or semi-gloss sheen. The higher the sheen, the more resistant the paint is to humidity and moisture. Make sure you scrub down the walls well – soap scum can mess up a good layer of paint.
Another thought: Be careful about getting impatient with the drying of a paint in a bathroom. Have good ventilation and wait a few days before using the shower or bath in that particular bathroom. Semi-gloss paints might take 2-4 weeks before they are fully cured, and high humidity from a bath or shower will inhibit the process. If you rush this drying time, the paint will to feel rubbery and may peel off easily.