Cut bacon crosswise into 1/4-inch pieces. In a 10- to 12-inch frying pan, stir bacon frequently until browned, 4 to 5 minutes. With a slotted spoon, transfer bacon to drain on towels. Reserve 2 tablespoons drippings in pan.
Put spinach in a large bowl. Rinse and pit plums and cut into 1/2-inch-thick slices.
Set pan with drippings over high heat. Add mustard, vinegar, and sugar; stir, then add plums. Heat until boiling, about 1 minute; turn plums over once.
Pour hot plum mixture over spinach. Mix and lift with salad fork and spoon. Sprinkle with bacon and add salt to taste.