I have been primarily using wool batting for the last few quilts I have done. I use either Dream Wool or Hobbs Wool and I have yet to have a problem. Except for the last quilt I did. The fabric I used for the background on the top was EXTREMELY loosely woven. It was a dark charcoal (not that the color matters).Before and immediately after I washed it I had bearding. No bearding on the back though, which is a fabric from Free Spirit, so very nice quality, higher thread count and tighter woven. The background, terrible quality. I attributed it to the loosely woven fabric which did not tighten up at all after washing.
I looked at the last quilt that I did with Hobbs and it has no fuzz or bearding at all. Another case for not only buying the best quality fabric that you can afford but also using common sense when selecting fabrics. I knew when I picked up the charcoal that it felt rough and loosely woven but I ignored those facts because I liked the color, texture and I thought that with washing it would improve. This fabric was purchased in my LQS.