I have made several Bow Tucks, and always use fusible Pellon, and quilt the whole thing, including the outer pocket. I feel like it makes everything more stable, since I tend to toss mine in the washer and dryer when needed. I carried one of mine for probably 2 years, and it looked as good as new, when I finally got tired of it.
When I first started making them, I grid-quilted them, but that takes longer than I want to spend to do it well. Now, I quilt with fast, curvy lines, and I love it. It's faster, and prettier, I think. :-D
Here's a picture of the one I'm carrying now...