How do you paint marlite in bath room?

The whole idea of melamine is that not much will stick to it, not even paint. The paint might go on initially, but it won't stick. You could try roughing the surface with sandpaper and coating the roughened surface with a good automotive primer. Use a 300 grit wet/dry paper, and keep it wet while you're sanding, then after you've knocked the shine off, wipe it all down to remove the dust, let it dry thoroughly then put the primer over the surface. After the primer has dried thoroughly you can put whatever paint on it that you want. A better solution would be the cultured marble tub surrounds. They hold up much better in a damp location and they are really good looking.