Heat oven to 350°F. Line 2 large cookie sheets with foil; spray foil with cooking spray.
Separate dough from both cans into 8 rectangles; press perforations to seal.
In medium bowl, place shredded chicken, bell pepper, spinach, garlic, 1/4 cup of the Parmesan cheese and 1 cup of the Alfredo sauce; stir until combined.
Place 1/2 cup chicken mixture onto center of each rectangle. For each bundle, bring up 4 corners of dough and fold over top of filling; gently press dough together to form a ball and hide the filling. Repeat with remaining rectangles and chicken mixture. Place 4 on each cookie sheet.
Bake 20 to 25 minutes or until golden brown. Meanwhile, heat remaining Alfredo sauce. Cool bundles 5 minutes before serving.
Serve bundles topped with warm sauce and remaining 1/4 cup Parmesan cheese.