After a bit of google research I settled for a sling for the mat rather than a bag. I thought after class when you are trying to pack up quickly, trying to get the mat inside a bag would be rather awkward. With the strap you just put the loops around the end, tighten it up and away you go.
This was really simple to make. Just cut 3 pieces of fabric 6" x 30", join together. Fold both short ends in by 1/2", then iron long ends in half, straighten, then fold both ends in towards the centre crease, then in half again to create a long strap. Sew around all edges with 1/4" topstitch. When done, just take one end of strap, loop it around the strap around 12" from end, when loop is formed sew together in a crossed box shape to hold. Repeat for other end. Now the loops can be loosened to take the mat and then cinched together to hold it tightly for carrying.
I used some cotton sateen that I had bought online and didn't like.