Thank you to everyone who responded. I think the winning solution for me is....
 
Headsets in large hanging bags submitted by Mary Beth Molloy of North Branford Intermediate School.
 
"We've put the headsets in large hanging bags, one to a bag, and they are
stored on a rack in my back office. I can take the whole rack (or put it
on a cart) if it needs to travel. One advantage to this system is that it
will prevent the spread of lice throughout the headsets, since they are
stored in individual bags." 
 
 -- I especially appreciated the lice comment.
 
Tell her what she's won Bob!
 
She's won the undieing gratitude and respect of a fellow library media specialist AND A NEW (toy) CAR!
 
 
Some other good ideas:
 
Thanks everyone for your responses and a special thanks to Mary!
 
Thomas Vaghini
Library Media Specialist
Stafford High School