Preheat the oven to 375 degrees F. Spray a 9×5 loaf pan with nonstick spray.
Over a large bowl, sift together the all-purpose and whole wheat flours. Stir in the baking powder and the salt. Pour in the beer and stir until a batter forms. It will be thick. Stir in the grated white cheddar and crumbled bacon. Spoon the batter in the greased loaf pan. Pour the melted butter over top.
Bake for 50 to 55 minutes, or until the bread is golden brown and set in the middle. Remove the pan from the oven and let cool for about 30 minutes. Slice and serve.