Bodrum Turkish Baths

I was there on an RS tour and I don't think anyone partook of a Turkish bath there (but rather in Istanbul). How about asking either your hotel, tour guide (if you have one), or better yet check out what's recommended in the Lonely Planet Turkey book (they typically list Turkish baths and do at least a little writeup). For sure it will be "an experience" you won't forget! I partook of two in different places (maybe Bodrum was even one of them, although it was years ago and I can't remember) and they were quite a different experience and the setting was quite different (I really enjoyed one in Istnabul that was in this really old marble place that was quite atmospheric). You can even go totally "local" if you feel comfortable (meaning go to one that serves locals as opposed to tourists) but it will be a very different experience yet (not that English is much spoken in other baths, but much so in touristy ones).

Just read a bit about what to expect first..it will make the experience better.

Surprisingly enough one of the best(and authentic) hamams is the old Bodrum Municipal Hamam.I believe it is now in private hands though now, but still has a high standard.It is easily found on the main road opposite the bus station.From the harbour just walk directly north away from it(with the sea to your back)and keep walking for about 7-8 minutes and you'll see it-or any shop you ask will point you in the right direction.
http://www.bodrumhamami.com.tr/bodrumhamami
Be aware that in a traditional hamam, rather than just a tourist place ,that there are separate rooms for men and women;they aren't mixed sexes, but don't worry you'll be safe and well looked after and staff will speak enough English to help you.It is open until c.23.00 so you could even do this at the end of your day before evening dinner.