Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 20 to 25 minutes. Drain and transfer to a large bowl.

Preheat oven to 350 degrees F (175 degrees C).

Mash potatoes with 1/4 cup butter until butter is melted. Beat sour cream and cream cheese into potato mixture until smooth; mix in 2 cups Cheddar-Monterey Jack cheese. Spread potato mixture into a 9x13-inch baking dish; sprinkle with remaining 1 cup Cheddar-Monterey Jack cheese, 2 tablespoons butter pieces, and bacon bits.

Bake in the preheated oven until bubbling, cheese is melted, and edges are crisp, 20 to 25 minutes.