Segregated baths? that won't do. The main reason he wanted to go to the baths was to look for spell fragments. After checking out the men's bath he turns around and heads out. Once out he would walk into the woman's bath. He imagined that as soon as a girl saw him they would all start screaming and throwing stuff, but you never know. Barring any interruptions he would disrobe and head into the bath like nothing was up. The spell fragments were only on elves, so the first thing to do in the lady's bath would be to look at the ears and find the elves.