Pre-heat the air fryer to 390ºF and pour a little water into the bottom of the air fryer drawer. (This will help prevent the grease that drips into the bottom drawer from burning and smoking.)
Combine the bourbon and brown sugar in a small bowl. Place the bacon strips in the air fryer basket and brush with the brown sugar mixture. Air-fry at 390ºF for 4 minutes. Flip the bacon over, brush with more brown sugar and air-fry at 390ºF for an additional 4 minutes until crispy.
While the bacon is cooking, make the burger patties. Combine the ground beef, onion, BBQ sauce, salt and pepper in a large bowl. Mix together thoroughly with your hands and shape the meat into 2 patties.
Transfer the burger patties to the air fryer basket and air-fry the burgers at 370ºF for 15 to 20 minutes, depending on how you like your burger cooked (15 minutes for rare to medium-rare; 20 minutes for well-done). Flip the burgers over halfway through the cooking process.
While the burgers are air-frying, make the burger sauce by combining the BBQ sauce, mayonnaise, paprika and freshly ground black pepper to taste in a bowl.
When the burgers are cooked to your liking, top each patty with a slice of Colby Jack cheese and air-fry for an additional minute, just to melt the cheese. (You might want to pin the cheese slice to the burger with a toothpick to prevent it from blowing off in your air fryer.) Spread the sauce on the inside of the Kaiser rolls, place the burgers on the rolls, top with the bourbon bacon, lettuce and tomato and enjoy!