Rinse fish thoroughly in cold water; pat dry. Place fish in a greased shallow baking pan. Top with sliced onion, bay leaf, and 2 teaspoons salt. Bake, uncovered, at 350° for 1 hour.
Sauté chopped onion in butter in a large skillet until tender. Add mushrooms, tomatoes, chopped parsley, thyme, remaining salt, and pepper. Cook over medium heat until vegetables are tender. Drain oysters, reserving liquid; set oysters aside. Stir oyster liquid into sauce mixture. Cover; simmer 20 minutes. Stir in oysters. Remove from heat.
Pour sauce over fish. Bake, uncovered, at 350° for 30 minutes or until fish flakes easily when tested with a fork.
Transfer fish to a serving platter. Remove and discard bay leaf. Spoon sauce over fish; garnish with parsley sprigs.