We had a wet bath in our PUP for 9 years and it was fine. We are smaller people though so that could factor in. I had a few small bath mats that stayed in the bottom of the shower so when you used the toilet, that dirt and grime didn't get into the shower. And no shoes were allowed in (well I'm Canadian so we don't wear shoes anywhere in the trailer).
When it was time to shower, the mat at the bottom was taken out and shaken outside and swapped out if it was dirty. Then after the shower I rinsed and squeegeed out the shower and put a mat back in and it was ready to go. Shower curtain was pulled into a corner and has a tie that held it there. It was made of some material that dried very quickly.
It was cramped for me to shower off the little ones, but we managed. It sure beat having to truck kids and all our stuff to the campground showers and potentially wait in line. And beat having to take a kid out at 3am to pee.