My reusable bag of choice is the string bag . When empty, they fold up really small, but they can carry a ludicrous amount of shopping and their soft handles do not cut into my fingers. I bought mine from Organic Ally
Her bags are made from unbleached organic cotton and are of course fully biodegradable.
She sells bags with either long or short handles.
The short handles are great for supermarket runs, the long handled bags can be hung off your shoulder for more leisurely shopping but I don’t like them as much as the short.
Turtle Bags also do a 100% ORGANIC cotton, short handled string bag in Natural unbleached cottonMade in India, Fair Trade Assured. They can be bought on line or from the Half Moon Health Store in Huddersfield