I've used a lot of wool batts and have never had this problem---most of the quilts I've made with wool batts do have flannel backs- not plain cottons but I've never had this happen- I've used the dream wool batts and the hobbs wool batts I love them both- maybe it has to do with the size needle/thread you used? were your backs pre-washed? I used my first dream wool batt 7 years ago- and the quilt still has not had this happen- it's been washed a dozen or so times (at least) ... but it does have a flannel back---the top is regular cottons though---no bearding anywhere. did you by chance not quilt it as closely as you are supposed to? I would *guess* if you are supposed to quilt every 2"-4" and actually have 6+" between quilting lines there would be the possibility of fiber migration & bearding. I hope you figure out what happened/how to fix it