>>9789693
The "normal" headbow headbands will fit into wider letter holders like these, you can hang them off a hanger and hang that in your closet, or use an S-hook if there is one hole at the top. If you can find the clear ones and only keep max 3 headbows in each pocket, you can hang them all up and it'll be easier to see at a glance all the headbows you have.
Fascinators, canotiers, minihats, etc -- clear boxes seem to be the only route, I'm afraid. I know someone uses a mannequin head to model them, but that's not going to keep a lot of them organised.