Preheat your oven to 350°F (175°C).
In a skillet over medium heat, melt butter and scramble the eggs until just set. Season with salt and pepper.
Place the bottom halves of the bagels on a baking sheet.
Top each with scrambled eggs, a slice of cheese, and a slice of bacon.
Cover with the bagel tops.
Bake for 5–7 minutes until the cheese melts and the bagels are warm.
Garnish with chopped chives if desired and serve immediately.