I store all of my "empty" bobbins in a framed coin purse I got free in a Mollie Makes magazine. I store my wound bobbins with the thread using a rubber band. I can't remember where I saw this, but it is BRILLIANT!
Thread one end of the rubber band through your bobbin. Pull that end through the other end and pull tight. You now have a bobbin "button" on one end of your rubber band. Now wrap the "non-button" end (both bands) all the way around your thread and over the bobbin, as if you were buttoning a button. Gosh, I don't know if I explained it right. Sure wish I could find it online. I'm using it now and just LOVE it. Neither the bobbin or the spool of thread unravel and are kept together. You can even wind multiple bobbins and store several on one spool until you are ready to sew.