In a glass, microwavable measuring cup, combine the corn syrup, two tablespoons of butter, one tablespoon of sugar, bourbon and pinch of salt. Microwave on high power until the mixture is melted and bubbling, about two minutes. Give it a good stir to combine. Set the sauce aside to cool a bit and thicken.
Grease two oven-safe ramekin baking dishes (4 - 6 oz. in size) and set aside.
Melt the butter in the microwave.
In a clean bowl, whisk together the half and half, egg whites, sugar and vanilla. Slowly pour the melted butter into the mixture and whisk until smooth.
In a separate clean bowl, pour the batter over the bread cubes and stir until the bread is completely coated with the batter.
Place half (divided equally) of the coated bread into the prepared ramekins. Sprinkle with half of the chocolate chips. Divide the remaining half of the coated bread between the two dishes. And top each dish equally with the remaining chocolate chips.
Place the dishes into the basket of your air fryer.
Air fry the bread pudding at 325 degrees F for 12 - 14 minutes, until it is puffed and golden brown.
Serve the bread pudding topped with the bourbon butter sauce.