I have some reusable cloth bags I use for shopping. The plastic bags I’m bringing to the store to recycle are mostly things like bread bags and other packaging, not necessarily plastic grocery bags.
Although people not reusing their plastic bags was exactly why California decided to just do away with plastic bags altogether. The first bag ban got rid of the thin single use plastic bags, but instead you could pay 10 cents for a thicker “reusable” plastic bag at the checkout. The idea was that people would then bring the reusable bag back to the store to use on their subsequent shopping trips. But in practice most people weren’t doing that, because for most people 10 cents is a trivial amount of money, so they were just getting new “reusable” plastic bags every time they went shopping. Since those bags were thicker than the old disposable plastic bags, they were probably consuming more plastic than before. So now we’ve gotten rid of those and switched over to paper bags.