Preheat the oven to 400 degrees F (200 degrees C). Stir cream cheese, Parmesan cheese, mayonnaise, garlic, and spinach together until evenly mixed; set aside.

Press pizza dough onto a baking sheet and brush with 2 tablespoons of olive oil. Sprinkle with 1 teaspoon Italian seasoning. Bake in the preheated oven until golden brown, 10 to 12 minutes.

Meanwhile, heat 2 tablespoons of olive oil in a skillet over medium heat; cook bell pepper and onion until tender, about 5 minutes. Season with 2 teaspoons of Italian seasoning; stir in shrimp and cook until heated through.

Spread spinach mixture on cooked pizza crust; spread shrimp and vegetable mixture on top. Slice into pieces to serve.