Place peeled garlic in a microwave-safe bowl with 1 tablespoon of water. Microwave on high for 1 minute. This step will remove the harshness from the garlic, but the flavor will remain.
Remove garlic from the microwave oven and let it cool for 2-3 minutes before handling. Slice thinly and set aside.
Preheat your grill to medium-high heat or 400 degrees F.
Divide pizza dough into 4 equal-sized pieces and roll them into 8"-9" rounds on a floured surface. Place two of the dough rounds on a pizza stone.
Brush olive oil on each round and top with equal parts of clams, garlic, crumbled bacon, and cheese. Return to the grill over low heat. Close lid and grill until cheese is melted and crust is golden brown, about 6-8 minutes. Repeat the process with the next two pizzas.
Once cooked through, transfer pizzas to a large cutting board. Top with fresh arugula and cut each into fourths. Serve immediately.