In the UK, they have to charge for the reusable bags by law, so people are trained to bring their own reusable bags because it costs them money if they don't.

Do they not charge for them in California? It needs to change people's behaviour, not just the bags.

We use fabric bags that last a lifetime and most people did before this law came in because a lot of people care about the environment. Although a lot don't, but caring about their finances helps drive others to do the right thing.