I always carry a rucksack with me, wherever I go. So if I need to remember to get something with me occasionally, I put it either in the rucksack directly, or on top of it. Since the rucksack also holds the keys, I cannot forget the rucksack.
For a while I even carried a strong big reusable bag in the rucksack (all the time), especially when I had to live without a car.
Usually I keep those bags in the trunk of the car. When I go shopping, after parking, I pick up the bags. The count of bags depends on the estimated amount of things to buy (I have only two bags, I usually do not need more).
If I forget to take them from the trunk, or I assume that I will only buy a small thing, and end up buying a full cart, then I go with the cart at the trunk and transfer the products to the bags there.
How do I remember to get the bags back to the trunk after emptying them at home, after shopping? I fold them and put them with the rucksack. Whenever I go out the first time, the bags will end-up in the trunk again.