I go to a monthly craft/sewing/quilting meeting and needed a press board to take with me. I found this great tutorial on-line: Missouri Star Quilting I used an 18" x 24" piece of plywood; wrapped an old towel around it; and then made a cover for it. It works great & I use it a lot.
Then I saw this at Joanns folding cutting/pressing mat
I really liked it, but I didn't want to pay that much for it. It's kind of small and I already had a press board and a mat. But it did give me the idea to make a bag to carry my board and mat plus my ruler.
I just made a flat bag a little bigger than my board. I used a piece of a fabric I found in my stash. It's a tablecloth that I had bought on clearance at Kohl's for $7.00. It's very sturdy and was leftover from when I made shopping bags. It was exactly the right size to made it double thickness. I made straps from some red 1-1/2" wide nylon webbing that was in my stash and just happen to match the fabric.
It's does a great job of carrying everything.