Glass is also theoretically close-loop recyclable but it's again cumbersome and expensive. It's usually downcycled into building materials.
I'm already skeptical of the overall impact of recycling in general; I feel as though it makes people feel like they're helping the environment while turning attention away from the mass polluters. I'm definitely cynical, but I'd really like to be proven wrong on that last point.
So the outcome of banning disposable bags is a whole lot of extra plastic being disposed.
Since I grew up in a state where you got free plastic bags, and went to college in another such state, it took some adjustment. But it's not really that hard - pretty soon you just remember to bring a bag when you're shopping, in the same way that you might remember to bring your wallet.
It's very hit or miss. When I go to Ralph's by me during the day, they say no reusable bags. When I go at night they're fine with it. My Trader Joe's only allows reusable bags if you bag the groceries yourself; the employees aren't supposed to touch them