Pet sitting is probably your best option. Plane turbulence can cause unneeded stress on your fish. Not to mention the constant jostling by other people going, "ooh, lemme see your fish!!"
... oh wait, airlines usually don't allow liquids anymore.
So leave your buddy at home and find someone to pet-sit. :) Good luck!
And for traveling information about transporting Bettas by car, here's the article I wrote: http://www.bettafish.com/showthread.php?t=24667