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Good on you for tackling the problem in this way!
If you search for 'newspaper bags', there are quite a lot of designs around that you might copy. People are making these to sell, but you could knock up a few to give away free if you needed to. You can probably find a design online somewhere for folding that doesn't require glue.
Another idea for a bring-your-own fabric bag product is to sell a fabric bag or a set of several sizes in a climber's chalk bag or a modified version of it. You could make groovy and sedate versions for all ages. When shoppers leave the house, they just clip it on their belt or whatever. Chalk bags used to be really popular a few years ago, and they could be again, as a fashion statement of self-sufficientishness.