You could always call the Contemporary guest services desk and ask.
The camp store at the Wilderness campground is the best bet. Catch the boat by the docks behind the pool.
The last time I was there was just before they rehabbed the Food and Fun center, but they used to sell individual slices of bread (and PB and Jelly). No, you wouldn't want to feed an entire family this way, but if you just want to make a daily PB&J for your fussy eater, this works. I remember the cost being less than $1 per sandwich, which beats any sandwich price you're going to find anywhere in the World. Just bring one of those semi-disposable Glad-Lock sandwich containers to carry it in and you'll save several dollars on lunch for the day.
I don't think I would consider a taxi off property (high cost, bleh!). But, if you have a car, there is a Winn Dixie grocery store on 535 just north of the downtown Disney area that is normally priced.
You might also check the convenience stores, (which must have some kind of contract not to gouge guests). Unfortunately, none are really close to the Contemporary; the fastest is probably just on the other side of the Magic Kingdom parking lot. I guestimate the distance at about a mile each way, a pretty good hike and no promise they have bread.
Brian