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.