I had to cancel my elk trip to Montana this year due to a bad hip. But in years past I have put my TD recurve and arrow cases in my rolling dufflebag, surrounded them with boots, clothes etc. and checked it. My binoculars, ranger and paperwork went into my daypack which was my "carry-o" for the trip. By the time you are ready for a hunt the bow and the arrows are a "matched set". If you got to your destination with bow but no arrows you would be SOL. So they might as well be in the same checked bag.
I used to ship bow and arrows via FedEx to the FedEx office near where I was hunting. I used their tracking utility and was able to verify that my bow and arrows had arrived BEFORE I departed for my flight. That way if I had to I could take a back-up bow with me if the package was lost or delayed. I never needed that plan B. But I found that once I got the TD recurve it was easier to put everything in my roller dufflebag.
JMC