This is a very easy project. All you need is some bubble sheet (I used 60 x 30 cm), something to make straps (I used a 146 cm strap), and a sewing machine. I guess it's possible to sew it by hand, but the machine is faster and easier. Enjoy!

Step 1: Design and Cut

According to the piece of bubble sheet you've got, design your bag - I found a piece of 30 x 60 cm, and I think it's a good size: I made a square bag, 28x 28 cm.
When sewing plastic there's no fraying, etc., buy it look nicer if you make some kind of hem. Just fold it in and sew, 0.5 cm would do.

A general tip - this material is a bit more difficult to sew than other plastics. The bubbles tend to get in the way and jam the machine. Sew slowly and punch little holes in the bubbles while sewing.

Step 2: Making the Straps

To make the straps, you can use another kind of plastic bag, from a more sturdy plastic (you can look at some examples here - https://www.instructables.com/id/upcycling-different-materials-into-bags; https://www.instructables.com/id/Upcycling-Plastic-Bags). I used a piece of strap I had at home. The length I used was 68 cm per strap, plus 2-3 cm extra per side.
I usually use a chalk to mark fabrics. Here I use erasable markers. Mark the exact point the strap is attached on the other side of the bag before you start sewing.
I usually sew at least a square shape attaching the straps, here I only made one line, on top of the hem I made earlier. You can use either zigzag or a regular stitch, as long as use go over it at least a couple of times.

Step 3: You're Done!

Important tips: Keep away from children! If they're too young it's a chalking hazard; if they're bigger they'll pop your bag!
You can try this with different kinds of bubbles - please post pictures of your projects!