Phayre will pretty much only wear bows on nylon bands. Every once in awhile she'll wear a lightweight lace headband, but never a fabric head wrap (such a bummer because there are so many cute ones out there!).
When I had just about finished P's nursery (you can see her full nursery tour here), I realized I didn't have anywhere to display her bows. I got a random idea to hang them from her picture ledges. I only thought of it because I literally had no where else to put them. So I grabbed some twine and mini clothes pins out of my craft box (they were leftover from a baby shower that I had thrown). I used packaging tape to attach the twine to the shelf (that's how last minute and random this idea was!). Because the nylon headbands are so light, the packaging tape has actually held up! Twine, mini clothes pins, and packaging tape... doesn't get much easier than that!
Phayre does have some head wraps that I often try to make her wear (and she rips them off... sigh). I keep those in little glass jars.
I didn't have to put much thought into Sloan's bow storage because Belle and Blush did all the work for me! I love Sloan's bow organizer, I can see everything and it's easy to get her bows on and off. I also have some glass apothecary jars on her dresser that hold her headbands.
I hope these ideas help you find ways to organize your little lady's bows or headbands!