Prepare the oven. Preheat the oven to 400°F. Line a large rimmed baking sheet with parchment paper.
Cook the eggs. Melt the butter in a large skillet over medium-high heat. In a bowl, beat the eggs with the milk, salt, and black pepper.
Pour the egg mixture into the skillet and cook, stirring often, until the eggs are almost completely set. Keep them a little soft so they are easier to spread over the bagels.
Prepare the bagels. Arrange the bagel halves in a single layer on the prepared baking sheet.
Add the toppings. Spoon the scrambled eggs over each bagel half, gently pressing them down so they stick.
Sprinkle the cooked bacon and shredded Colby Jack cheese on top.
Bake. Place the baking sheet in the oven and bake for 5 to 8 minutes, or until the cheese is melted.