Bring a pot of lightly salted water to a boil. Cook carrots in boiling water until soft but firm to the bite, about 10 minutes; drain. Transfer carrots to a container with a lid; add onion and bell pepper.
Stir tomato soup, sugar, vinegar, oil, Worcestershire sauce, mustard, salt, and black pepper together in a saucepan over medium heat; cook and stir until sugar is completely dissolved, about 5 minutes. Pour soup mixture over vegetables.
Cover the container and refrigerate vegetables, 8 hours to overnight.