Here's an update on how my little project is going. Told one of my friends what I was up to and she sent me a patch that she had lying around. Since my sewing skills are a bit rusty, I broke out the hot glue gun and glued the patch to the bag. As I was gluing and pressing the patch down, some of the glue seeped through the edges. I tried to wipe the excess off, but it just ended up leaving a white residue around the sides of the patch.
You can't tell from the picture, but the white residue works as a cool border. I call that a happy accident.