I just use My Touring Ortlieb panniers , they pop right off, I lock the bike up, and put them in the cart.
then at check-out, i lay them on the feed belt 1st.
the store credits a nickel for every store carryout bag I don't use..
then packed, I put hem back on the bike and ride home..
Grocery bag panniers are square botom so kicking them while pedaling becomes a problem
with other than old beach cruiser bikes, with quite Long chainstays..