I have to be in on this challenge. Just the other week my shopping bag split and i lost a tin of spaggetti. It rolled straight onto the main road. The annoying thing is it wouldnt of happend had someone took the time to design a pushchair or pram friendly reusable bag.
I have a habbit of hanging the carrier bags on the handle of the buggy. but you cant with reusable bags. (not sure if this is the case in America).
That's how I like to carry my bags when I use my stoller.
The plastic bags over here aren't very good. At least in my opinion, they are way to thin and rip if they are too heavy with forces you to use more bags then you would normally.