Begin making the dressing while the potatoes are grilling: In a 12-inch skillet over medium heat, cook the bacon until crispy, 8 to 10 minutes, turning occasionally. Drain the bacon on paper towels. Pour off all but 3 tablespoons of the bacon fat in the skillet. Add the celery to the skillet and cook for 3 minutes. Add the sugar, and continue to cook until the sugar is dissolved and the celery is cooked through, 2 to 3 minutes, stirring occasionally. Add the vinegar and 1/2 cup water; cook until bubbling and slightly thickened, about 2 minutes, stirring occasionally. Reduce the heat to low. Add the mustard, pepper, and salt, stirring until combined, and cook 2 minutes. Remove the skillet from the heat; add the bacon pieces and the onions, tossing to coat with the dressing.