Showers are one of the lovely modern inventions the Society for Creative Anachronisms incorporates into medieval camping events. Roman bathhouses supplied soap and towels, but SCA showers do not.
So the members of the Society have come up with ways to make our bathing kits look period. I found a nice wooden bucket at a yard sale, and I keep my bath supplies in it for events. Baskets from thrift stores also work well. If you are concerned about displaying modern containers, a washcloth tucked over the mundane items can maintain the medieval image.
Some Society members prefer to grab their bathing supplies and throw a towel over their shoulder, but many would prefer not to put on and take off several layers of clothing. A compromise has given rise to the bathing chiton, an interpretation of early Greek garments made from bath sheets. This is my bathing chiton, and I have pulled the front open to show that there are actual arm holes concealed behind the towel drape.
In my post about Forms of Greek Dress, I discuss how the dorian chiton is made from two pieces of fabric buttoned or sewn together. A Bathing Chiton is sewn at the shoulders and sides, with an extra bit of fabric over the chest. In the diagram below, the left image shows where you sew the seams, and the right image shows the location of the seams when you wear the garment.
I have not yet seen a man wearing a Bathing Peplos, but the concept is the same.