Just remember these things.
It takes upwards of 500 years for a plastic bag to decompose. Paper bags come from trees ( hint : deforestation). It takes more energy to make and recycle paper bags.
So go for reusable cloth bags. Have them handy in your car or in your bag all the time. More importantly, if that person at the check out starts to put your items in a plastic or paper bag, just say, ‘thank you but I have my own’.