ProTip: Keep a bag of bags in your car. When you go to a store with carts, skip the bagging and just put your items back in your cart. You can bag them at your car in peace with no rush. The cashier will appreciate you, the bagger will appreciate you, and the other folk in line will appreciate you.
Honestly, byob feels a lot nicer too. If you're bagging your own groceries, you're not faffing about with a new bag every 3–6 items, you're not concerning yourself with double-bagging, and it just goes by a bit faster. If you have a couple insulated bags, you're not as worried about routing your trip to get the refrigerated and frozen stuff last (although this might still happen if you get dairy milk and meat, idk). If you're taking the groceries home in your car, you have a lot fewer bags to worry about and don't have to check to make sure you have all them and nothing's rolled out. And carrying them in is easier because you can physically fit more groceries into a trip. Small things, but they do add up to a nicer experience I think.
I bought a used shopping basket at a thrift store - you know, the type with handles that stores often offer for free use. I stays in my car trunk. If I only need a few items it comes into the store with me. Useful in the store, after checkout, then into the house. Cashiers think it’s funny that I have my own.