Refuse the plastic bag and carry your own!
The easiest thing you can do is to refuse plastic bags when you go shopping. It's automatic for a shopkeeper to hand these out at checkout so politely stop them and tell them you will use your own or that you will only accept paper. Here are some super convenient, cool looking options that are easy to pop in your everyday bag so you always have it with you.
Folding Reusable Grocery Bags 5 Pack - 21.6"x13.8" Capacity - Washable, Waterproof Nylon holds Heavy Groceries - Foldable Tote Bag is 4.3"x 4.3" Folded - Eco-Friendly Shopping Bag fits in Pocket