Preheat oven to 450 degrees. Place a pizza stone in center of oven to heat while preparing toppings for pizza (for at least 30 minutes).
To make alfredo sauce: Melt butter in a medium saucepan set over medium-low heat. Cook flour 30 seconds then add garlic and cook about 30 - 60 seconds longer just until mixture is lightly toasted and fragrant.
While whisking slowly pour in heavy cream and milk. Cook mixture, stirring constantly, until thickened. Remove from heat, stir in Parmesan cheese, then season with salt and pepper to taste. Cover to keep warm.
To assemble pizza: On a floured sheet of parchment paper flatten, stretch and shape pizza dough into a 13-inch round, while creating a thicker outer crust. For a fluffier crust let it rest 10 minutes.
Pour half of the white sauce over dough round, then use the back of a spoon to spread into an even layer coming within about 1-inch of the edge. Sprinkle shredded chicken over sauce layer, then pour remaining sauce evenly over chicken.
Sprinkle top evenly with Mozzarella cheese then sprinkle with chopped bacon. Brush outer crust with olive oil.
Transfer to pizza stone (I use this pizza peel) in preheated oven and bake about 12 - 14 minutes until crust is nicely golden. Remove from oven, sprinkle over parsley, cut with a pizza cutter into slices and serve warm.