Preheat oven to 500°F (260°C). If using a pizza stone, place it in the oven while preheating.
On a lightly floured surface, roll out 1 pound pizza dough into a 12-inch circle. Transfer the rolled dough to a pizza tray, a 12-inch round baking sheet, or a pizza peel lightly dusted with cornmeal.
Spread 1/2 cup Alfredo sauce evenly over the surface of the dough.
Top with 1 1/2 cups shredded mozzarella cheese, 1/2 cup grated Parmesan cheese, 1 cup shredded cooked chicken, and 1/4 cup cooked and crumbled bacon, if using.
Bake for 12 to 15 minutes, or until the cheese is melted and the crust is golden brown.
Remove from the oven and garnish with 1 teaspoon chopped fresh parsley, if desired. Serve hot.