I decided to post this under Suggestions instead of under a post regarding a first trip to Prague and the Blue Danube.
I agree on the height of the bathtub being dangerous, and the slippery floor, too, because the shower door is only half. Take a 6 foot man whose arms are long, cannot fit between the wall and the door with any room while washing. Water is bound to splash, and the door is not sealed.
This is what we do. Usually we have 3 bath towels or hand towels (if not, ask for one more). We place one of the hand towels in the tub while running the water to get the temperature right. We stand on it while showering and drying.
When drying, before I use the towel on myself, I sort of dab the towel on the water beads on the door to prevent more water on the floor, and then dry myself. On the floor we have the bath mat. If my husband bathes first, he then puts his bath towel on the floor, creating more space so I can try to get out of the tub on my own. Most times the bath mat provided slides on the floor if it's not wet. I'm 4'10", with one knee replacement and one knee needing one, and two hips and back pain. Trying to hold onto the bar which is on the long edge of the wall in the tub, it is too far for me to hold on to and lift my legs, one at a time out of the tub.
I've tried sitting on the tub, pulling each leg over, but the edge of the tub is multi-layered and not easy to sit on. Without a safety bar on the back wall of the tub area, just not easy to get out of the tub.
But, short of carrying my own slip proof decals to place in each hotel bathtub (and maybe forgetting to pick them up when we leave), we just let the hotel take care of the very wet towel in the tub. These tubs have been that same size, style since I first went to Germany in 1961, and no European country has changed it since. We had visited many countries on that first tour of duty (almost 4 years, so I honestly can say, things have not changed as far as bathtubs. Except, hotels now have porcelain instead of stainless steel
In Ireland in 2012, I was literally stuck in the tub because I did not use this procedure of putting a towel in the tub and the floor was so slick from a lot of water even though we both were careful not to get water on the floor.
I did get a stool from housekeeping, but it was the library style that had wheels. No way was I using that. I really couldn't put my foot on top, as it was higher, and the leverage was off. I used the extra towels they brought to put on the floor of the tub and floor and over the edge of the tub and I sat and slid the few inches to the floor.
Be safe, and whatever works for you, please share as I have done.