Reusable bags aren't an option for you? We have several of them and just put them in the trunk. If I forget to bring one (which happens 1-4 times a year) I buy a new one for 2€, replacing an almost broken one.
The amount of learned helplessness in this thread is astounding. I bought a pair of collapsible reusable bags years ago for $5. I use them every week and they're as good as new. The stronger construction means that each one is replacing at least three disposable plastic bags with every trip. You don't need disposable bags. And yes, I have a cat, and disposable bags are shite for litter, because they always, always have holes.
I imagine all the "I can't fit bags in my pockets for my impromptu shopping trips" people posting when mobile phones first became popular: "Are they expecting us to put these in our pockets?! All the time!? Just in case someone calls???"