Public toilets are few and far between in Bodrum and the only one I ever remember seeing is one on a small square around the corner from St Peter's Castle (on Karatiina Sokak).
These toilets are supervised by a very friendly man who will charge you for the pleasure of using the toilet (approx 1 YTL but possibly less actually).
Try to have the correct change to avoid the man becoming slightly grumpy! There is a sink area to wash your hands and there is a ready supply of the lemon scented cooling/cleaning lotion. This toilet is very clean and nice smelling.
Remember also that toilet paper must not be put down the toilet in Turkey as the sewage system is unable to cope with that type of solid waste (water pressure issues and an often seen problem in the countries from the Med and Aegean). Tissue needs to be put in the small bins found in every establishment. These are generally cleaned out regularly during the day and night so there should be no collection of mess - if there is just tell the staff, it will be sorted.
These are traditional western toilets folks so no squatting (phew!!), Bodrum is quite advanced like that but when you go on excursions this might not always be the case soremember to bring some spare tissue (just in case) and if you are squemish about squatting watch what you eat and drink :-)

