I roll my binding up and leave a hole big enough for my hand. I put the roll of binding on wrist and let it feed as I sew, it doesn't tangle and works great.
Sharon W.

Another way is to fold it back & forth, put it in a bag - eg a small JoAnn's bag - and hang it from a knob or hook in front of where your sewing machine is sitting. Out of the way, not on the floor.