Getting the bag off your back and onto your bike is always best. You'll be more comfortable, and if you have bulky groceries they won't dig into your spine.

For awhile I went with the topeak trunk bag and rack. Now I just have a milk crate strapped to my rack. If I'm riding to work, I just throw my bag into the milk crate. If I'm going to the grocery store, my normal shopping bags fit securely in the crate as well.