I had a similar bungee cord incident, only it didn't happen on my bicycle...it happened on my motorcycle! I was on a trip, so I had a piece of motorcycle "luggage" attached to a rack on the rear of my bike with long bungee cords. We had stopped to gas up somewhere, and I must have needed something out of my bag so I had unhooked the bungees. It wasn't until we were back on the road and another rider in our group behind me noticed that BOTH of my bungees were hanging down and dragging along the highway. I thank my lucky stars that those cords did not get tangled up in my rear tire, otherwise that would have been a really ugly situation.

I'm glad the OP wasn't hurt as a result of something like this.