Boil the potatoes in salted water until fork-tender, about 10–12 minutes. Drain and let them cool before cutting into bite-sized cubes.
Cook the bacon in a skillet until crispy. Transfer to a paper towel-lined plate and crumble once cooled.
In a large bowl, mix together the mayonnaise, Dijon mustard, salt, and black pepper until smooth.
Add the cooled potatoes, crumbled bacon, chopped celery, and diced red onion to the dressing.
Gently toss everything together until the potatoes are evenly coated.
Cover and refrigerate for at least 1 hour to allow the flavors to meld.
Serve chilled or slightly warm, garnished with extra bacon pieces or chopped parsley if desired.