If you absolutely must do it, the PVC tube is a good suggestion. But I would really think seriously about forgetting about trying to fly with a one piece bow.
With the limit of a maximum of one checked bag on most airlines you are looking at paying for a second bag in order to bring your bow. And it will be an oversize bag to boot, so it could easily end up costing you $100 EACH WAY to bring it with you. If it were me, I would use that $200 to put toward the purchase of a take down bow and pack that bow inside my other checked bag. It's a great excuse to buy a new bow, and we all need all the excuses we can get!
The other draw back is that as an oversize item, your bow will be much more suseptable to not making the flight with you. Not having your bow arrive with you would really put a damper on your trip. Do you really want to put the outcome of your hunting trip in the hands of a baggage handler?
As an alternative, is there any way to ship the bow ahead of time? At least you would know before you even left that your bow arrived safely and is there waiting for you.
Good luck!