Meredith,
I would not recommend trying to walk there from any Walt Disney World resort, except perhaps one of the Plaza Boulevard Hotels. It would be quite the march. I would suggest taking a cab, if that is doable. Dependent upon where you are leaving from, it should not be more than about $15 each way, probably less.
Of course there is also their delivery service. I assume you saw one of my answers that refers to that, but for anyone reading this reply, here is that information again;
Goodings will deliver your grocery order to your hotel. I have not used it myself, but if you visit their website at
www.goodings.com you will see how to order. There is a minimum order requirement, as well as a fairly significant delivery charge. It appears that if you are ordering a lot, it might be worth it.
Have a magical vacation!