Place torn bread in a food processor and pulse until fine crumbs form. Transfer bread crumbs to a large bowl and add milk; set aside until bread is completely soaked.

Place onion, red bell pepper, and garlic in a food processor and pulse until finely chopped; stir into bread mixture. Add turkey, egg, parsley, 1 tablespoon mustard, salt, and pepper to bread crumb mixture and mix well. Cover bowl with plastic wrap and refrigerate for 1 hour.

Preheat oven to 450 degrees F (230 degrees C). Spray a rimmed baking sheet with cooking spray.

Shape turkey mixture into 1-inch balls; arrange on the prepared baking sheet.

Bake in the preheated oven until firm and cooked through, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let meatballs stand for 5 minutes.

Mix yogurt, mayonnaise, and 4 teaspoons mustard together in a bowl; serve alongside meatballs.