Bodrum is well served by the intercity bus lines. You can get here from any major transport hub in Turkey. A lot of the services are night buses getting you into town in the early morning. If you're hacking along the coast the usual minibuses run regularly from all points east or west.
Bodrums nearest airport is not a major one but internal flights with THY (Turk Hava Yollari) operate between Imsik and Istanbul or Ankara in the summer.

Perhaps the nicest way to arrive is via the ferry from Datca, 2 hours across the bay at the end of the Marmaris Peninsula. This car and passenger ferry operates every day in the summer and 2 or 3 times a week out of season. You'll arrive in Bodrum at about 11:00 am and get a great view of the castle and marina into the bargain.

History | Bodrum