Put the potatoes in a large saucepan; cover with cold water and season with 1 teaspoon salt. Bring to a simmer and cook until tender, 8 to 10 minutes. Drain and transfer to a large bowl.
Meanwhile, cook the bacon in a medium nonstick skillet over medium heat, stirring occasionally, until crisp, about 10 minutes. Remove the bacon to a paper towel-lined plate using a slotted spoon. Pour the drippings into a small bowl and wipe out the skillet.
Return the skillet to medium heat and add the olive oil and 2 tablespoons of the reserved drippings. Add the shallots and cook, stirring, until softened, about 4 minutes. Whisk in 2 tablespoons each vinegar and water, the mustard and sugar. Bring to a simmer.
Pour the warm dressing over the potatoes; season with 1/2 teaspoon salt and a few grinds of pepper and toss. Add the remaining 1 tablespoon vinegar, the chives, dill and bacon; toss again. Serve warm.