Even here in suburbia we've bicycled for our groceries, three baskets per bicycle, allowing for at least six bags, possibly more depending on how we pack the bikes, to be transported the less-than-a-mile home.
If it's really less than a mile, why would you cycle? I'd rather just take a decent rucksack and walk. You can't carry all that much safely on a bike.
I suppose you'd save ten minutes each way travel time, but by the time you get the bike out, lock it up at the shops then put it away when you get home, it probably isn't any quicker over all.