Preheat oven to 400ºF (200ºC). Lay the bacon out in a single layer on an aluminum foil-lined baking sheet and bake until golden brown and crispy, about 20 minutes.
In a medium mixing bowl stir together the chicken, mayonnaise, mustard, black pepper and cayenne until completely combined.
Preheat oven to broil. Lay the bottom halves of the bagels out on a baking sheet. Top each bagel half with a scoop of the chicken salad and top with a slice of cheese.
Broil until the cheese is melted, about 1 to 2 minutes. Top with bacon and close up the sandwiches. Slice in half and serve.