Combine first 7 ingredients in a small bowl; stir with a whisk until blended.
Combine bulgur and 1 cup boiling water in a large bowl. Cover and let stand 30 minutes; drain. Stir in 1/2 teaspoon salt.
Steam green beans, covered, 5 minutes or until tender. Drain and plunge beans into ice water; drain. Place beans in a large bowl. Add bulgur, tomatoes, parsley, onion, and oil mixture; toss gently to combine. Serve at room temperature, or cover and chill.