Snub plastic bags; take your rucksack to the supermarket. Ask your supermarket to remove unnecessary packaging.
Ah, the old plastic bags vs bin liners debate rears its head again. You see, when the Paddy Republic introduced its tax on plastic bags, they found that sales of bin liners went through the roof, because people used to use plastic bags for bin liners but now they were too valuable so they didn't do that any more. And bin liners are worse than plastic bags for landfill sites because they take longer to break down. The same argument applies here.
Now, I get round this by reusing bags as much as possible, and not taking those extra little bags to put fruit in and so on, and buying things with less packaging (Co-op are particularly good, so I shop there as often as I can), but if I know we're running out of plastic bags for bin liners, I go to the Co-op and get one of their biodegradable plastic bags for my shopping and subsequently, for my bin.
I'm not sure this is a great plan, but it's the best I can come up with.