1. Preheat grill to 350° to 400° (medium-high) heat. Cook bulgur according to package directions. Toss together bulgur, 2 Tbsp. oil, 1/2 tsp. salt, and 1/2 tsp. pepper; spread on a baking sheet. Cool completely (about 15 minutes); transfer to a large bowl.
2. Toss together shrimp, 1 Tbsp. oil, 1/4 tsp. salt, and remaining 1/4 tsp. pepper. Thread shrimp onto skewers. Toss together peppers and 1 Tbsp. oil.
3. Grill shrimp and peppers, covered with grill lid, 2 minutes on each side or just until shrimp turn pink. Brush onions with 1 1/2 tsp. oil, and grill, covered with grill lid, 1 minute on each side. Slice peppers. Cut onions into 1/2-inch-long pieces.
4. Toss together bulgur mixture, peppers, onions, lemon juice, and remaining 1 Tbsp. oil and 1/2 tsp. salt. Top with parsley and shrimp.