We use fusible fleece in our shop for the purses and bags we display as store samples. It comes in a couple of thicknesses, still thinner than quilt batting. The fusible is ironed to the outside fabric; it adds loft and stability to the bag. Additional stabilization is not necessary. You can quilt it if you like, but not necessary. I love this product and use it in all my personal bags as well.
Cindy