It has taken me the better part of the week, but here is a set of instructions, drawings, and photos which I hope will make it fairly easy to sew a bento bag of your own. If you use 40-inch + wide fabric and cut across the width of the fabric, you can make two bags from the material, which is what I did in this session. It will be easy to make it larger or smaller depending on your needs.
Lots of pics of the inner seams after the cut, especially the folds and seams forming the bottom of the bag.
Once you have made the side seams, you can roll and seam the tube for the drawstring. I made that seam about 1/2 inch wide, but it is easy to make it wider.
I made the handles out of contrasting fabric, about 1 in wide, seamed and turned. You could also use handbag strapping available from the fabric or craft store. Or no handles at all, if you prefer. :)
Sew a seam along the dotted lines to shape the bottom of the bag.
I've turned the bag so you can see the bottom seams.
The drawstring in place and the handles sewn in.
I gave the bottom some further support by adding a plastic insert which is just laid in the bottom of the bag. The plastic was made by cutting up an empty plastic cat litter bottle. Nothing like a little recycling. :)
And the finished bag! This first set took me about 3-4 hours from inital cutting, sewing, pressing, and figuring out how to form the bottom of the bag. I think future bags will go a bit faster.
This is a good way to use up smaller pieces of fabric, and would make a nice patchwork project, too, if you wanted a fancier bag. I've gotten a lot from this community, I hope this little contribution is useful.