Jim,
What Bjorn said works. I would add - I used to fly to Cabo every year and take my 2 piece, 11' 6" surf rod with me. I bought a heavy duty rod tube that is adjustable for different lengths. Never had it crushed or damaged, even going International and through Customs both ways. I had to check it as one of my bags unless I wanted to pay extra. I don't know how that works out now - check with the airline.
I would put the bow in a fleece sleeve and then in the tube. I used it this past Winter like that, thrown into the back of the pickup when I went out hunting. My rod tube has foam padded ends and is lockable. I had a label with my name and address on the outside and inside of the tube. Bon voyage!