We do the same, but we also take bags to the grocery store (usually knitted fabric or heavy duty plastic with handles, i.e., like a handbag) and sack our own groceries. I prefer that to getting new bags each time. We also minimize use of small plastic bags for produce.According to Greg's article and options here, it's disposable paper bags.
I reuse the little plastic grocery bags for trash bags so that I don't have to buy trash bags. I use them as liners for my trash cans, I use them to collect trash and food scraps in the kitchen. I don't just throw the bags away.
Various stores now take returned/used bags, and I suspect they just trash them, but I'm not sure.