I don’t live in California, and we don’t have a legal ban in place, although one is coming, but stores started either charging for bags or refusing to give them out several years ago.
All grocery stores sell sturdy bags (woven plastic or cloth) for around $2. I have a few of those, which I bring whenever I go shopping. I don’t have a car, and it’s still not an inconvenience. You just have to train yourself to remember to do it, which… after forgetting once or twice is not that hard. I no longer have the overflowing “bag of bags” which used to be a source of guilt and annoyance, so that’s nice.
When I go to the corner store for an item or two, I often just carry them home in my hand. For example, in the evenings, you’ll see at least one person per block carrying a bottle of wine, for just this reason. Because this is a city-wide phenomenon, it does not look at all out of place. It’s really not difficult or strange at all, although I grouchily predicted that it would be before we started. I got over it pretty quickly.