Bodrum is on Turkish time, UTC+3, like the rest of the country. What changes from city to city is the daylight.
Turkey keeps one time zone across roughly 1,600 km, so the clock in Bodrum matches Istanbul exactly while the sun rises at a different moment. The figures above are calculated for Bodrum's own coordinates and update as the date changes.
Bodrum sits on a peninsula on the Aegean and is Turkey's best-known sailing town, the usual departure point for a gulet cruise along the coast. The town itself is built around a castle on a spit between two bays.
In antiquity this was Halicarnassus, and the Mausoleum here was one of the Seven Wonders of the Ancient World — the word 'mausoleum' comes from it.
Bodrum is in the Aegean region of Turkey.