Thanks so much guys!
The more I think about it, I realize that I'm actually after 2 bags. 1 to go in my EDC purse and the other for my wilderness kit.
I carry a packable reusable shopping bag in my purse. It has big handles so I can carry it on a shoulder uner an arm, but I would rather have something with proper shoulder straps and a drawstring closure. Something I could throw a jacket or sweater into, or carry groceries more comfortably.
For my wilderness kit, want something that I can wear on my belt, around my waist or that will attach to my pack, so I can forage as I go, without taking off my pack.