Love that idea Jolene!
Another idea - while the main stores I know of that encourage using cardboard shipping containers are Aldi and Costco - I would bet that any grocery store would allow you to use some containers that they would just be discarding
And then one more idea - since I compost, it isn't the end of the world if I have to take a paper bag because I can shred it and add it to the pile. Especially in late spring and summer when I don't have a lot of browns to add the pile yet, a couple extra browns help to keep the pH of the pile balanced