Last October, we didn't have a car so we just walked to Goodings (about 25-30 mins), bought our groceries and took a $6 cab ride back.
Yes, there are cheaper groceries around, but if you have to take a $15 cab ride (each way) or pay $20-30 for a service, then the groceries end up costing more.
A better option might be to rent a car for one day. Pick it up at the airport and drop it off in WDW. It'll cost about $30-40, but getting to your resort faster and being able to do a few more things other than grocery shop might make it a worthwhile expense.