Cook the potatoes: Bring a pot of salted water to a boil. Add the halved new potatoes and cook until fork-tender, about 15-20 minutes. Drain and let cool slightly.
Prepare the dressing: In a small bowl, whisk together the buttermilk, mayonnaise, Dijon mustard, apple cider vinegar, garlic, salt, and black pepper until smooth. Adjust seasoning to taste.
In a large bowl, combine the cooked chicken, potatoes, crumbled bacon, arugula, radishes, and fresh herbs.
Drizzle with the buttermilk dressing and gently toss to coat.
Serve immediately or refrigerate for up to a day for flavors to develop further.