Oh, Beth Ann, your comment about using park showers just reminded me of a couple of other tips. Bring along a pair of flipflops or, even better, water shoes, that you can wear right into the shower so your feet are never in contact with the floor. I personally like the water shoes because I don't like having to mess around with socks and shoes in those tiny shower areas, and water shoes keep my damp feet from getting dusty when I walk back to the tent.
I also recommend a cheap plastic basket with handles to carry your shampoo, shower gel, towel, clean undies etc to the shower area to keep everything dry and within easy reach. My plastic basket cost $.99 at the dollar store and is worth it's weight in gold because I can set it on the bench, or hang it from a hook, and keep everything up and out of the sometimes less than pristine floor area. I also wear a pair of sweats, or a loose T-shirt dress, sans undies to the shower to make getting undressed quick and easy. Changing into your actual clothes and shoes is easier in your own environment.
And a final hint: go for your shower either very early in the morning (say around 6 am) or mid morning (around 10:30 or 11am) to make sure that you have hot water! Otherwise, your shower can be unexpectedly refreshing and your teeth will be chattering.
And, on a brighter note, the vast majority of park showers are just fine as long as you keep things simple and don't attempt much grooming/dressing in them.