Aloha scorpio47,
The small dehumidifier is an option, and Margaret's idea of bringing an electrician in the double switch the light and fan is workable too. and depending on the light, you may be able to run a pull on/off switch from it for less cost (I'd do two switches on the wall personally).
You can leave the door open with the fan on for 5 minutes of so right after the shower to get circulation in, and the humid air out. Then leave the door a bit open to have some exchange of air.
Even Marie will say that there are situations where you may need to have the bathroom door open for a while during the day for adequate ventilation.
I'd be sure to wipe down the room well with a purification/disinfectant of your choice to keep on top of the musty smells until it starts getting enough ventilation to balance it itself.
Much Love, Shawn
