So, on one of my RV forums, someone was talking about cling for their window for privacy. Hmmm, that would probably work for shower doors as well.
It wasn't easy and it doesn't look perfect, but it looks better than water stains. Now I just have to hope that the steam of the bathroom doesn't cause it to fall down.
I still have two extra rolls, so if it stays up, I may consider doing the closet doors as well, since I hate all the mirrors in the bathroom. Think I'll wait a while before springing that idea on Dave :)