I have used everything from left over batting, lightweight pellon, Decor Bond and whatever I have on hand. I have really good success with the outer portion of the bag in just batting and close cross hatching quilting. Then I do the lining of the bag with the pellon in either the fusible fleece or the Decor bond. Since the Decor bond is pretty stiff, I usually use a piece of batting on the fabric first and then fuse the Decor bond to the batting. The stiffer lining makes the bag seem a little sturdier. ` I like the quilted look of the bags, so just using a little basting spray on the batting works great to hold it while I quilt.
I also have not washed a bag yet...But now that you mention it mine probably needs it...!!