It depends, did you put your first coat on yet ? If not and the room hasn't been painted in a while then I would prime first. The reason is your wall are probally real dry. Without priming the paint will just keep soaking into the walls and you will need several coats at least to cover. By priming first you will seal the wall preventing the paint from soaking in and provide a good surface for the paint to bond to. If you already applied your first coat without pimer, then appliy a second if it looks ok fine if not apply a third.
you should always apply at least two top coats. And as posted in many cases a primer is also a good idea. For baths use Zinsser's PermaWhite to prevent mold and mildew. You can have this tinted to any color you want. Use it for both coats, since it is also used as a primer.