I occasionally travel with wet clothes. This Saturday I probably will, as I'm going down to FLL for a quick beach day, and flying back the same night. I usually keep a couple of plastic bags (usually a couple of produce-style ones from a supermarket, and then a larger standard plastic trash bag; sometimes a gallon ziploc if it's only one or two small items), and double bag and do my best to tie it off, to keep moisture out of other things. When I go home this Saturday, my bathing suit will likely be wet or damp; since that's the only item, I may try the ziploc. I'll also do my best to dry it somewhat in an airport restroom using the hand dryer. When I get home I will rinse everything and then let it dry before doing laundry.

Mold/mildew should not be a major issue unless you are traveling 12+ hours. In my case I am only traveling 3 hours

-J.