Cook rice according to package directions, omitting salt and fat.
Combine water, bay leaf, and quartered onion in a large Dutch oven; bring to a boil over medium-low heat. Add mussels; cover and simmer 6 minutes or until shells open. Remove pan from heat; drain mussels. Discard any unopened shells. Remove top half of shell from each mussel; discard. Place mussels on a serving platter; keep warm.
Heat oil in a nonstick skillet over medium- high heat. Add bell pepper, chopped onion, and jalapeño pepper; sauté 4 minutes or until tender. Remove from heat; stir in vinegar.
Spoon 1 cup rice into 4 shallow soup bowls. Divide mussels evenly among bowls of rice. Sprinkle pepper mixture evenly over mussels.