There is much evidence that bags are not much of a problem, most people reuse them eg for garbage bags in the house. Other items are more wasteful, for eg when you buy a drink you get a thick plastic bottle which you use for 2-3min then throw out??? Or fast food plastic boxes which are similar.
I would shop less I think at the super market, since I wouldn't go there if I didn't have my greeny bag with me which I would need to go back to the car to get.
But the point is, these bags are reused as garbage bags, so basically instead I'll buy them and then put the rubbish into the bags which I bought and they would go into landfill, so its the same thing in the end???