I haven't had this problem very often only on 3 occasions years ago, but I too have noticed that this occurs on overly thinner fabrics. I have used a lint roller to collect all the fibers instead of hand picking them, then washed and dried them and after about 3 washes the batting "gathered up" as I'd call it and it stopped.
In my case, such an issue has never been a problem that has been ongoing for the life of the quilt. The best advice I learned and took from myself to avoid this is to never use ultra thin fabrics in quilting no matter how pretty they are because even though the bearding will stop, if the quilt is loved and used well, that fabric tends to wear out quicker than normal, and then the batting will really, really start coming through.
I had a very upset nephew many years ago who recieved a quilt from me that had a very thin fabric in the borders and it wore out quicker because of the thin thread count. From that experience plus 2 others after that in the same year, now I don't ever use thin fabrics in quilting unless it is going to be a wall hanging and exposed to minimal (to no) laundering.
Explosive blessings, abundance and inspiration to you all!
- The Creative Seamstress