I don't think it did that much because they didn't ban plastic bags in the fruit and vegetable section where you can peel bags off from a roll. They also require you to individually bag each fruit or vegetable type at most grocery stores I've seen. They're always free too.
That means if you buy a few apples, oranges, avocados, cucumbers and tomatoes you're using 5 plastic bags of substantial size. If you get fresh romaine lettuce or something bushy they have plastic bags that are bigger than the old plastic bags they used to provide at checkout.
You're also not limited to fruits and vegetables. Some people will put bread and other lighter items in these plastic bags in case they didn't bring a bag of their own into the store and have a couple of things to carry out but don't want to use a cart.
The only thing the ban did was to get most grocery shoppers to bring their own bags to carry or cart your items out at checkout. In this case, sure you saved a number of bags no question about it, but in the grand scheme of things I don't think it solved much.