I take my one piece selfbow Pigger on every hunt, including those that require flying. The short answer is, it cost an additional $75 each way or $150 per trip to fly. My belief is Pigger leads a charmed life that permeates to those who hold her, she alays goes. With our history of critters taken while carrying her I don't usually give it a second thought. It is a matter is convenience and cost.
That said, one time flying to and from a AK moose hunt I put Pigger into a fly rod case with a bunch of Sage, Simms, and Winston stickers on it and a Sage rod, tied a piece of leader with a fly to the tip of Pigger, then took her as a carry on. Checked her with the large carry on's as you enter the plane and never had a problem. However, the lady at the scanner in Fairbanks ran it through twice then gave me a smile while chuckling and whispering to her co-worker as she handed it to me. Hey, I did say she lives a charmed live. Really wouldn't recommend anybody else trying it.