Scrub live mussels under cold running water. Using your fingers, pull out the beards that are visible between the shells. In an 8-quart Dutch oven combine 4 quarts of cold water and 1/3 cup of the salt. Add mussels; soak for 15 minutes. Drain and rinse. Discard water. Repeat twice.
In a large Dutch oven cook sweet pepper, onion, and garlic in hot butter over medium-high heat for 4 to 5 minutes or until onions are tender. Add Cajun seasoning; cook and stir for 2 minutes more.
Carefully add wine. Bring to boiling; add mussels. Cook, covered, for 5 to 7 minutes or until shells open and mussels are cooked through. Discard any that do not open.
Use a slotted spoon to transfer mussels to a large shallow serving bowl; set aside. Stir tomato, oregano, and thyme into cooking liquid in Dutch oven; heat through. Pour mixture over mussels and serve with bread. Makes 4 servings.