Rick, I used to have a rough wooden frame compost bin close to the willow tree and after finding the roots in the compost as you did, I thought I would try putting a couple of layers of landscape weed cloth on the bottom, that helped but the roots then went up the sides and into the compost, then I put it on the bottom and up the sides for about a foot or so, and stapled it to the sides of the bin, that worked quite well.
