I have found if you stitch across the lower portion of the outer bag fabric and fleece backing at about 1/2" intervals going all the way to the bottom of the fabric you will not need anything more. It stabilizes it and makes it stand up.
I am not sure these will show in order but the black outer bag that is laying flat shows the stitching. The single floral bag is a completed bag with the stitching. The three bags are soft and made before I started stitching the lower portion of the bags.