First, get rid of a bath mat. They only hold water. If you want some friction on the floor of the shower, then get the stick-on bath tub non-skid stickers for the floor. Water can't get under them and that reduces a lot of wet!
Second, if you have glass shower walls and doors, squeegie down the glass and the walls after EVERY use. We do... always. Not only does it remove water, it also keeps the shower doors (and walls) clean, no soap or lime build up. We also squeegie our shower at home after every use too. Always! Never miss. And the shower is always clean and dry.
With our new 5er, I've started wiping down the walls with a towel after use to dry it completely. Then hang the towel outside.
Third, when taking showers run your exhaust fan. Even if it's a tiny one, it's better than nothing. It will pull a lot of humidity out will will remove potential for mold later. Keep it running a short while after the shower is over too.
Forth, keeping a couple windows cracked, even if you are running an air conditioner or the furnace, helps ventilate the camper and removed humidity.
And FYI, we "live" in our camper from early March through November, sometimes even longer depending on how old-man winter is costing us in heat. We keep water in the tank and use the shower almost every day (2 of us). We are on our 4th camper now, and we've never had icky shower doors or walls. Discovering the squeegie was the best thing we could have ever found. It takes discipline to use it EVERY time though. But it only takes a few seconds to do it, and it saves so much aggravation later.