Our stores just give out NEW, unused bags, for all grocery items bought, each time we shop.
Some use paper, some use plastic.
All new.
Then, they typically have a recycling bin located at the store exit, if you’re into that sort of thing, so you can bring their (or, other store’s) bags back.
That’s what most of the stores I shop at do - new bags. If you request paper, you’ll get them. The only store I shop where you MUST have your own bags, if you want to bag, is Aldi’s. What I have noticed is they leave bins of empty boxes around the aisleways where they’ve restocked shelves & people will pick up a box or two (or three) for their groceries.
Food Lion has some great reuseable bags - I got a couple for 50 cents each. They enlarged the bags recently, so they’re now 99 cents each. I use the smaller ones all the time, not just for groceries - I’ve even used them for carrying tomatoes when I had too many to pick in the garden for my usual large bowls. As I said, any meat products or anything likely to cause dampness (frozen veggies/fruits that melt a little) go in single use bags before going in my reusables, so I don’t worry about them being “contaminated”. If they need a thorough cleaning, just flip inside out & wash.
My mom is into recycling the plastic bags so some do get recycled. Some people cut the bags into strips and make ‘plarn’ and crochet things with this plastic yarn, including bags that are reusable.