I would suggest you look at the ski bag idea versus the fly rod or PCV tube option. A big difference between a fly rod and a bow is a fly rod you can carry on. The bow must be checked and with most airlines that means a checked bag fee of usually $25 to $50 each. So I would want to pack the bow with other items like - clothes, knives, calls, arrows, etc - so I only had one bag to check and one bag to deal with. The ski bag or something similar allows for that. And of course, knives and broad heads also need to be checked.
Ohh if you are going to bear country, a sidearm needs to be checked too and you cannot bring pepper spray at all on a plane. You would have to buy it at your destination.
And I know we all have that one special bow, but I think I would go with the takedown. I think you will be happier. Travelling with a tradebow on planes is very doable, but it isn't as simple as we tradition folks usually migrate too. A takedown will not require any special purchases and fit in anything your arrows will. I just wrap my takedown in my hunting clothes for padding, put a rubberband around my arrows, put the knive and BHs in a small hard tacklebox, and toss it all in a big duffle bag with everything else. Never had a problem...
Good luck and have a great hunt.