Clean the bathroom walls with trisodium phosphate and a sponge. Trisodium phosphate is a general cleanser that works well for painting prep work; trisodium phosphate residue does not react poorly with fresh paint.
Stick painter's tape to trim or bathroom fixtures that you want to leave unpainted.
Apply bonding primer to the laminate surfaces. Start at the edges, using a paintbrush. Once the edges are primed, use a medium-nap roller to apply bonding primer to the laminate wall surfaces. Bonding primers are formulated for better adhesion to glossy surfaces like laminate, glass and ceramic. Wait for the primer to dry before proceeding.
Paint the laminate bathroom walls using oil-based interior paint. Oil-based paint holds up better against moisture damage common to bathroom spaces. As with the primer, paint the edges first with a brush, then use a medium-nap roller on main surfaces. If you're using an oil-based paint with a glossy finish, consider foam brushes and foam rollers for fewer visible brushstrokes and roller marks.
Apply a second coat of paint if there are bare patches after the first coat dries.
Peel off the painter's tape once the final coat dries.