Bring the water to a boil in an 8-quart stockpot. Add beans; cook for 1 minute. Add carrots; cook mixture 2 minutes or until crisp-tender. Drain; place vegetables in ice water. Let stand 1 minute or until cool; drain.
Combine sugar, vinegar, mustard, oil, and salt in a large bowl; stir well with a whisk. Add beans, carrots, bell pepper, and onion; toss gently to coat.