How can I paint my bathroom walls smooth and bump free?

Find out why the wall dips in and out. You may need to replace the sheet rock. To cover the bumps and dings you will need to spackle over the entire wall to make it smooth, then sand to remove any imperfections. It's really not as bad as it sounds since you will only be filling the crevices. Or...you could wall paper the room. They make a thick wallpaper base specifically to cover textured surfaces so the actual wall paper installs perfectly smooth. Check your paint and wall paper store. I'm sure they will help answer any questions.

Patch where your dings are and sand smooth. You can camouflage your wall by using a flat paint as anything with a sheen to it makes all the imperfections in a wall more noticeable.

They make a thick primer called Kilz High Build that will help smooth out a wall. Any deep dings I would fill with a spatula and joint compound first. I wouldn't use flat paint in a bathroom as it doesn't hold up to moisture, semi-gloss is a better choice.

Professional painters will come in and use a skim coat of drywall compound, then sand, prime and paint to even out small imperfections

Fill in rough spots then sand