I found a great tutorial for this over at How Does She?. You'll need some fabric, ribbon and velcro. She used home decor fabric, which would have been a bit less bendy... but I used the fabric I had on-hand and it still turned out pretty well.
You'll need two fabrics, one for the outside and one for the inside. Of course, you could use the same fabric for both, you rebel you. Cut the fabric to 10" x 13" so you have four pieces, two of each fabric, all the same size.
Pin the fabrics right sides together so you have your exterior and interior separate.
Sew the exterior bag with a 5/8" seam allowance around three sides, leaving one of the short sides open. Once you've sewed it, go back and do a zigzag stitch beside it for extra strength. This this is the Incredible Hulk of trash bags. Do the same thing for the interior fabric.
Trim the fabric next to the seam and clip the corners.
Turn one of the bags right side out. Shove it into the other bag so the right sides are together. Pin 'em in place.
Sew around the top of the bag, leaving a small section un-stitched for flipping it right-side out.
Just like before, add a zigzag stitch beside the straight stitch.
Pull the bags right side out by pulling the first bag completely out and then flipping them right-side out.
Top stitch around the top, which closes that hole we left...
Ska-doosh. That's what my three-year old says. The bag is done! Next, take some strong ribbon, about 10" or so. Cut it in half and burn the edges which will keep it from fraying.
Add some velcro to the ends...
Sew the other ends to the bag. PRESTO. You've got a bag... attach it to the back of your seat and expect that all the trash will just magically float to it.
There are a few steps to this project, but it was well worth it!