Cook the bacon in a frying pan over medium-high heat until crisp, about 2 minutes per side. Transfer to a plate lined with paper towels and let cool for a few minutes. Cut the bacon into thirds. Set aside.
Line two baking trays or pizza pans with parchment paper. Place the pizza dough on the trays and spread it evenly with the pizza sauce. Sprinkle with the mozzarella cheese.
Arrange the bacon on each pizza. Top with the tomatoes and dollop with the pesto.
Carefully slide the pizzas onto the grill grates. Bake the pizzas until the crusts are golden brown and crisp, 10 to 12 minutes. Remove from the oven, then sprinkle with the Parmesan cheese and arugula. Cut into slices and serve immediately.