I have made poly-batted quilts and never had any problem with bearding - I think I usually use Mountain Mist. However, I have a quilt given to me by my husband's grandmother, and it is bearding all over the place. The quilt top is a poly-blend and it is hand-quilted. I don't know if the hand quilting matters or not, but it seems like some of the bearding is occuring through the holes made by the needle.
I have used a lot of Hobbs 80/20 and I like that. I'm not sure if I have used warm and natural or not.