In a medium-sized bowl, combine the softened cream cheese, shredded cheddar, cooled and diced bacon, mayonnaise, sour cream, and optional hot sauce. Mix everything together with a spoon or spatula until it’s smooth and all the ingredients are evenly distributed throughout the cream cheese base. Season with salt and pepper to your liking.
Take your four bagels and slice a very thin layer off the bottom of each one. This creates a stable base so they don't roll around on the baking sheet. Place the bagel seeded-side down and carefully run a sharp knife around the inner circle, being careful not to cut through to the bottom. Use your thumbs to gently push the center bread out, creating a hollow space for your delicious filling.
Divide the bacon and cream cheese mixture evenly among the four hollowed-out bagels. Use the back of a spoon to spread the filling smoothly, leveling it off at the top. Arrange the stuffed bagels on a baking sheet and place them in an oven preheated to 375°F (190°C). Bake for 12-15 minutes, or until the tops are beautifully golden brown and the cheese is melted and bubbling.
Once the bagels are baked to perfection, carefully remove them from the oven—the filling will be very hot. For a final touch of flavor and a professional look, sprinkle the tops with the reserved bacon bits and some freshly chopped chives. These bagels are best served immediately while they are still warm and gooey.