Add the bacon pieces and cook until crispy, about 8 minutes.
Drain the bacon on a paper towel-lined plate and set aside.
Preheat the oven to 350 F.
In a large bowl, stir together the cream cheese, sour cream, chicken, shredded cheeses, all but 1 tablespoon of the scallions, all but 1 tablespoon of the bacon pieces, and the seasonings until fully combined.
Transfer the dip to an oven-safe dish and place in the oven. Bake until bubbly, about 20 minutes.
Once out of the oven, stir the dip to make sure everything is evenly combined.
Sprinkle the dip with the reserved scallions and bacon pieces. Serve right away.