It isn't the batting, if you used 100% cotton thread a lot of that fuzz is from the thread (top thread as well as bobbin) but your backing fabric can also contribute to it. I would say 95% of the fuzz is thread lint which is a big reason I don't use much cotton thread any more. I prefer poly as it doesn't create near as much lint. I have had a blob of lint get caught up in my bobbin tension spring and throw my tension off mid bobbin. Didn't realize it and spent a good amount of time taking the stitches out to redo. Thankfully frogging is easy when tension is bad. Pretty much swore off cotton thread then. I will use it if the color is right or a client insists. When I do use cotton, I try to make sure it is a super premium brand like King Tut, which throws lint too but not near as much. I also notice much more lint when I quilt a flannel back quilt. So I would say the fuzz you are seeing isn't from the batting but from the fabric and the thread. By the time your machine head travels over the quilt the batting is already encased between your top and backing fabric. As QuiltE said, it is best practice to clean out the bobbin area every bobbin change. Even when using poly threads which tend to produce very little lint.