You don't need dry ice - as if.

First of all, how are you hauling your groceries... panniers or trailer?

Find a soft sided cooler that will fit your equipment. Pack the densest at the bottom (ice cream/meat) then add frozen veggies and the like on top.
Heat moves - not cold. So if you insulate your MUST STAY FROZEN with the more "airy" frozen veggies you have a good 2 hours before your Rocky Road is puddled.