Helen
I have some links on companies that do land moves, but have never had any feedback or know anyone that has used them.
Depending on the weight and volume, is it possible you could use air freight to ship? Turkish Airlines has a comprehensive site on freight and associated costs however, they only ship freight from Gatwick to Istanbul so you would have to sort a local company for the transfer from Istanbul to Bodrum.
I do know and can recommend a private company that can handle the Turkish end.
Have a look here Turkish Airlines Freight Handling
http://www.thy.com/en/cargo/info.htm
Its one option to consider.
Merv