How to remove/prevent mold from forming in bathroom
First thing you want to do is verify that the fan is working. If there is an attic, you need to get up there and check the venting to the outside. If no attic, then remove the fan so you can stick your head up there and see what's going on with the vents. Poor ventilation is a major cause of mold and mildew. All my bathroom vents have 60 minute timer switches.

Next, mix 1 part bleach and two parts water in a spray bottle and spray down the whole bathroom. I don't usually use bleach, I use vinegar because it soaks into porous materials and bleach doesn't. In this case I'd use the bleach: spray, scrub, wipe down, spray, scrub, wipe down. Once everything is clean, wipe the floor down with vinegar. It will soak into the grout and prevent the return of mold.
Keep in mind that the walls are probably not made of that plastic. The plastic is a wall covering and there could be mold behind it. If any of the plastic is loose, pull it out and check for mold behind it. 

Last but not least, think about replacing all the caulk in the bathroom. Good luck.