Sauté bell peppers in oil in a 5- to 6-qt. pan over medium-high heat until beginning to brown, 7 to 8 minutes. Add garlic, saffron, and pepper and cook, stirring, until garlic is softened, 1 to 2 minutes.
Pour in 1 cup water, the clam juice, and wine. Cover, bring to a boil over high heat, then reduce heat and simmer about 10 minutes to blend flavors.
Return broth to boiling and stir in mussels. Cook, covered, over medium heat until shells open, 8 to 10 minutes; discard any mussels that don't open. Ladle into bowls, sprinkle with parsley, and serve with lemon.