Combine tomatillo salsa, chopped avocado, and cilantro; set aside.
Place bread in a food processor; pulse 10 times or until crumbs measure 1 cup.
Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add onion and bell peppers; sauté 5 minutes or until tender. Stir in 1/2 teaspoon fajita seasoning and 1/8 teaspoon salt. Cool.
Combine breadcrumbs, onion mixture, remaining 1 1/2 teaspoons fajita seasoning, remaining 1/8 teaspoon salt, tomato paste, turkey, and egg white in a large bowl. Using damp hands, divide turkey mixture into 4 equal portions, shaping each into a 3/4-inch-thick patty. Heat pan over medium heat. Recoat pan with cooking spray. Add patties; cook 4 minutes on each side or until done. Place 1 patty on bottom half of each bun. Top each serving with 1 1/2 tablespoons salsa mixture; top with remaining halves of buns.