First of all, you can't take a Mears bus anywhere. Mears isn't a city bus, you can't just hop on one and take it to a store or from one resort to another. And as for DME, you can ONLY take the DME bus from the airport to YOUR resort ... you can't choose to go to a different resort instead.
The best idea is a grocery delivery. There's Gooding's, a local supermarket that delivers, as well as Garden Grocer, a stand-alone delivery service. You don't have to wait around for the delivery, they deliver right to Bell Services (Gooding's does this automatically, with GG you have to request it but it's a standard thing to do). Bell Services will even keep your cold stuff cold for you!
We're not huge breakfast eaters, and most of our crew are sleepy-heads, so we save time and money by eating breakfast in the room; this has the added benefit of letting our kids ease into the day just like at home, rather than rushing them out the door to go to the food court and from there on to the parks.
Our orders have typically consisted of cold cereal, milk, OJ, bagels, cream cheese, yogurt, cheese sticks, deli-sliced American cheese, instant oatmeal (you can heat the water in the coffee maker!!!), bananas, grapes, apples, bread, PB, jelly, bottled water, and maybe some junk like Oreos and chips and soda.
The $15 or $20 delivery fee is MUCH LESS than a taxi would cost, plus you didn't have to waste time shopping and getting to and from a store and searching around and waiting in line there.
I've used Gooding's twice and was completely satisfied both times.