there should be plenty of taxis
but check the airport site
http://www.bodrum-airport.com/en/getting_there.php

If no one on here gives you any details to arrange a private transfer I'd advise you to try and find someone who does them on the Internet. In our area from Dalaman airport I know it costs nearly double if you just get a taxi outside the airport to Turunc, so suspect it will be the same in Bodrum. Have you tried asking whoever you have booked the accommodation through?

We have actually booked through directholidays so coach transfers are included but last year it took so long waiting at the airport to get the coach full so we though we would rather make our own way to hotel this year, many thanks for your replies
sandra

Have you been able to find the hotel's own website on the internet - they might be able to help you independantly of Directholidays? If you could find an email address for the hotel it may be worth asking.

http://www.propercars.com are recommended for private transfers and will cost less than a taxi from the airport.

Kedi