Steam the potatoes in a medium saucepan until tender, 12 to 14 minutes. Let cool for 5 minutes.
Meanwhile, cook the bacon in a large skillet over medium heat until crisp, 5 to 7 minutes. Let cool on a paper towel-lined plate. Break into pieces.
Whisk together the yogurt, lemon juice, ¾ teaspoon salt, and ¼ teaspoon pepper in a large bowl. Add the potatoes, bacon, watercress, and chives; toss to combine.