Thank you for the compliments. That is what is called a satin stitch or zig zag stitch. It's not difficult to do at all, just takes some time and you need patience.
I created the applique first and then stitched it onto the bag. I know I've had others ask me how I do them so I'll do a tutorial next time around. You can also see a basic tutorial at http://myhappycrazylife.com/how-to-applique/
, although I did not use her techniques. It is very similar though starting at step #11. Once you start, you will become addicted. I've been sketching out pictures of things I like on my google searches and then creating from there. That's how I did my Tennessee bag posted here. I'll post a tute soon!
Oh and originally, I saw someone else on Craftster do a simple tutorial and that's how I got started...but I can't seem to find their post. It was several years ago so it must be lost somewhere.
One will be coming soon...