1st -I use a ball winder to store my binding until ready for use. Just slip an empty toilet tissue cardboard over the winder and holding the binding gently in my hand, crank away and my bind is neatly wound around the cardboard.
2nd - I taped a small piece of batting to my long arm quilting machine and when I clip threads, just stick them to the batting and when it won't hold any more "strings", I simply gather them up, discard and I'm ready to go again.l