I found this excellent sewing tip and had to share it with you!
Try cutting pieces of 7⁄8-inch transparent plastic tubing just wide enough to fit over your bobbin thread, but in between the bobbin casing sides. You can get tubing (clear plastic hose) at the building supply or hardware stores. The tubing is inexpensive, is available by the foot or in 6-foot lengths which can be cut easily with scissors or a craft knife. Cut a slit for a flexible opening on each piece and wrap it around each of your bobbins to hold the thread securely in place.
I just recently had to clean up my bobbin-box disaster and wish I had seen this tip at the time!