In my last few trips, I’ve been flying with only one large duffle bag big enough for my takedown bow, arrows, quiver, and all my clothes. I also carry on a bag small enough to fit under the seat, with personal and expensive items like binoculars, iPad, etc. I have nice hard cases for my bows, but with the current charges for checked bags, it’s not worth it. Plus, I have had no damaged bows since I started using my giant duffle bag for everything, but I have had several scratched bows from some TSA agent tossing everything back into my hard case willy nilly and slamming the lid on a bow square or something on top of my bow.
Just be careful not to put anything sharp or otherwise against TSA regulations in your carryon bag.