When I was young, my parents were members at the local Coop grocery store. I don't know if they do this anymore, but they used to charge 5 cents for every plastic bag supplied by the store. Most people just started using reusable bags or started brining their own plastic bags from home. It worked. It would work again. No one complained. Better yet, people thought it was a great idea, and this was 20 years ago.
Even though the bags are truly recycled, the process of manufacturing plastic bags, then recycling them, and manufacturing them is wasteful. It wastes fuel, water, manpower, creates pollution. Why do it if you don't have to?
I have one of those reusable bags in the trunk of my car. I never use it. I never think to stop and bring it in the store. Mostly because I can get a bag in the store anyways, so it doesn't occur to me to bring in that bag. That's my fault, but if there weren't any bags available in the store, I would definitely remember to use the reusable, or at least go back to the car to get it.