I have 2 of these.

http://banjobrothers.com/products/cu...y-bag-pannier/

Grocery bags fit perfectly, they hold a lot and they have a shoulder strap for carrying. I bring one with me on commute days for quick stops on the way home. and use both for grocery and farmers market runs and for whatever else when I need transport extra stuff on my bike.

The reality is, If you live on two wheels (or try to) you need to have ways to carry stuff safely. Racks, bags, milk crates whatever you can figure out... they are your friend.