shower floor

Kill the mild spores. Then reduce the humidity inside your RV.

This works well for us as it is hard to do all of it as we age.

Do you have an exhaust fan in the bathroom? If so do you keep it on for 20 minutes after showers to reduce the humidity?
How about Tilex Daily Shower spray. But be aware it might make the floor slippery.
Another thought is to wipe down the walls and floor after showering. A good squeegee should do it.

Anecdotal evidence follows: My mother, who lived to 101, washed her feet in a Clorox solution every night in the tub. I do not know the exact formulation she used but she would put about 2-3 inches in the tub and then add small amount of Clorox. This was in a residential size tub. No mold and she was still walking the day she died.

I use a teak bath mat from Bed, Bath and Beyond. Had to cut it to size however.

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.

Have you tried good old BonAmi? (Not Comet, which can scratch)
That stuff removes dirt that other cleaners can't touch and is especially good on plastic.

We use a clear plastic mat that has holes and suction cups. It gets hung on the wall on a suction cup hook after each use to drain leaving the floor to drain and dry. Last person in the shower wipes the walls & door of the shower dry with towel. Using the fan in the vent while showering also helps. Couple times a season I will plug the drain, run in several inches of water, add bleach and throw in the mat and anything else that needs disinfecting for a good soak.

Suggestion: Add a timer to your bathroom exhaust fan. That way you don't have to stand in a breeze while you shower. Just turn it on for 30~40 minutes after you get out to dry it out.
I use one of these mounted in my ceiling which will happily switch 12VDC. linkaroonie

A dilute solution of household bleach in a spray bottle will keep most mold and odors at bay. Spray down the walls after your shower (doesn't have to be perfect).