This bag goes really quickly. It is made with cotton butcher twine I bought at the hardware store. The store where I bought the twine kept changing brands on me, but all butcher or "kitchen twine" turned out to be similar enough that it didn't cause any problems. My bag is light, easy to get my mat into, and works well when I am riding my bike.
Start by finding a crochet hook that feels like a good match to whatever string you end up using. Then work a flat circle until the circle has a diameter approximately an inch widerer than your rolled yoga mat. I did this with double crochet stitches. Then work in a V-stitch until the bag is as long as you would like it to be - mine is about an inch taller than my mat. I ended up doing a quadruple-crochet on my V-stitches because I like the airiness it created.
For the handle I did rows of 6 single crochets until the strap was long enough, then joined it back to the very bottom of the bag using slip stitches.