Will showering with the fan on and bathroom door open prevent mold?
A you hear all of the time mold needs moisture to get moving.
But, it also needs time, and a food source.
The Drywall and most surfaces give it that food source, but the time and moisture you can control.
If the house is new, the fan should be fit to size. I say this, but sadly it's often not true. Also, if the roommate likes steamy shower rooms, a good fan and an open door will likely remove the &quot;steam room like&quot; environment.
So, my opinion-ated answer based on these thoughts &amp; some known facts:
Fan &amp; venting:

Ensure the fan is the right size for the room. Please see what it is rated at, increase it to a higher cfm fan if need be.
Check the vent tubing, it should be rigid, not ribbed flexible like most contractors and builders, and homeowners use.
The shorter and straighter the run for the vent tubing, the better. Use 6&quot; vs. 4&quot; even. Also, make sure it is properly supported as moisture has to get out asap! this is the key really. It might be full of water, make sure it is not obstructed

The walls, cracks and crevices are where mold will grow, so a circulation fan in conjunction with the vent fan is a good idea. The home will need a source of fresh air or circulating it in the living space works, but is worse. Your best bet is to get it out of the house. A fresh source, (even opening a window a crack will suffice).
After the shower, wipe the walls down, keep the vent fan running for a while. you can install a timer too to control it and not have it run 24/7 (although that might be what you will need).
The sooner you keep the surface dry, the mold wont grow.