The first solution was a hamper attached to the back of the high chair.
The best part about this is that I can simply take this laundry and do a pre-soak before I wash it so that the food crusties and stains are minimized.
I also wanted to have a place for the clean bibs and cloths to be stored. I found the perfect container at Target . There's plenty of room to store all of our bibs and a bunch of cloths.
No more bibs/cloths all over the place, clean or dirty.