Preheat the oven to 425 degrees F (220 degrees C).
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add cauliflower; cover, and steam until tender, 8 to 10 minutes. Drain and let cool 10 minutes.
Combine mozzarella cheese, sour cream, mayonnaise, 1/2 the bacon bits, and chives in a large bowl. Add cauliflower; mix well. Pour mixture into a baking dish. Sprinkle remaining bacon bits and Cheddar cheese on top.
Bake in the preheated oven until cheese is melted and golden brown, 15 to 20 minutes.
