No. You cannot.
There is no direct flight to Bodrum from Hatay.
However, you have some options with connection flights.
From Hatay, there daily flights to Ankara, Istanbul and Izmir.
From Ankara and Istanbul, you can find direct flights to Bodrum.
And if you fly to Izmir, you can take buses to Bodrum which takes about 3-4 hours. about 6 years ago