Bring potatoes to a boil in a large pot of salted water. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain; transfer potatoes to a large baking dish.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain the bacon slices on paper towels; crumble and sprinkle over potatoes.
Heat a skillet over medium heat; cook and stir celery and green onion until celery is tender, about 5 minutes. Transfer vegetables to baking dish.
Whisk mayonnaise, vinegar, sugar, mustard, salt, and black pepper in a bowl until smooth. Pour mixture over potatoes and stir until well mixed. Sprinkle with Cheddar cheese.
Bake in preheated oven until cheese is melted, 20 to 35 minutes.