Preheat a griddle on low heat. Add the butter to the griddle, then place the bagel halves on the griddle, cut side down. Toast each side until crispy.
In a bowl, whisk together the eggs, salt, pepper, onion powder, and heavy cream.
On the other side of the griddle, set to medium heat, pour the egg mixture and scramble. Season with additional salt and pepper if desired. When the eggs are almost fully cooked, stir in the pre-cooked bacon bits.
Once the bagels are toasted, remove them from the griddle and place them on a steaming rack. Spread a spoonful of chili sauce on the cut side of each bagel half. Top with the scrambled egg and bacon mixture, then sprinkle Cheddar Jack cheese on top. These bagel bites are open-faced, so you won't use the top half of the bagels.
To melt the cheese, add a small amount of water to the hot griddle, being careful not to spray water directly under the steaming rack to avoid making the bagels soggy. Close the lid of the griddle or cover with a dome if your griddle doesn’t have a lid.
Once the cheese is melted, transfer the bagel bites to a platter. Sprinkle with chopped chives and serve immediately. Enjoy!