Baby Stroller Hooks, Universal Clips for Diaper and Mommy Bags, Heavy-Duty Hangers with Straps, Practical Stroller Accessory for Moms, Black-2pc

I don't know enough about ita bags to know what brands are reputable, but based on a google search it seems like there's a lot of options (both smaller purses and full size tote bags), that have a removable shoulder strap which attaches to a D ring sewn to each end of the bag (this listing shows a picture of one with the removable strap hanging down so you can see the attachment points fairly well). Maybe use a pair of "stroller straps" (velcro or cord loops attached to a carabiner, mostly marketed for attaching a diaper bag to a stroller: example of the velcro type, example of the cord type) to attach the bag to the back of your chair by those rings? (Velcro or cord end would go around the back cane on your chair, carabiner would hook onto the the bag.)