Heat oil in a large Dutch oven over medium heat. Add shallots and bell pepper; cook 5 minutes. Add wine and next 6 ingredients (wine through bay leaf); bring to a boil. Reduce heat; simmer 5 minutes, stirring occasionally.
Nestle fish into tomato mixture; top with mussels. Cover and cook 8 minutes; gently shake pan twice to stir mussels (do not lift cover). Discard any unopened shells and bay leaf. Sprinkle with parsley.