I guess it depends on whether you are talking about stiff headbands or the stretchy kind.
The stiff ones seems to work best hanging over a bar, while the stretchy ones are good on hooks.
I could see doing a little home project to tackle this; your DD is old enough to help build it, and it's always great to get a girl going on minor carpentry.
Get a nice smooth piece of wood about 1/2 thick that will fit on an open spot of wall in the bathroom; birch plywood is good, or a solid pine panel if you can find one. Frame it with moulding if you like, so it will look nice and have smooth edges, and paint it to match the decor.
Get several double coat hooks from a hardware store and screw them into position on the board, covering the area from the top to a bit below the middle, and spaced out by about 9" or so. These are for your soft headbands.
Also get a decorative towel bar that matches the hook hardware and fits across the width of the board (you can usually cut the bar itself to make it the right length; if it is metal you'll need a hacksaw), and mount that about 7" from the bottom of the board. That will hold the stiff bands.
Hang it at a height that is reachable, but where it won't get bumped into all the time, because the bar and hooks will project out a bit from the wall.
You could do this for about $15 if you go budget on the hardware, or you could go really pricey on it -- that's all up to you and your taste.
(If she uses ponytail holders you could also add some cabinet knobs to hold those.)