A2B Transfers seem to be the most popular at the minute...from both Bodrum and Izmir airports. I haven't read a bad review of them yet. Quite a lot of people in Kusadasi use them..and they've not let anyone I know down.
Here's a link to their prices from Bodrum Airport to Turgutreis...they give you the option of either travelling on their shuttle bus or by taxi.
We always use the same guy, very reliable, have used him for 5 years, he has an estate car for up to 4 passengers and mini bus for 5 to 15 pm me for details. Shame you're going this week, I need to share a transfer the following week.