In a 5-quart saucepan, bring 1 inch salted water to a boil; reduce to a simmer. Add potatoes. Cover; cook until tender when pierced with the tip of a paring knife, 25 to 30 minutes. Drain; cool slightly, and halve.
In a small skillet over medium heat, cook bacon until crispy, 3 to 5 minutes. Add onion. Cook, stirring often, until tender, 2 to 4 minutes. Remove from heat; add 3 tablespoons vinegar and mustard. Toss with warm potatoes. If desired, season with salt and pepper, and add up to 1 tablespoon more vinegar. Serve warm.