Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs; drain.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes; cook, stirring, until the garlic is slightly softened, about 1 minute. Drain the tomatoes, reserving 1/2 cup juice; crush the tomatoes with your hands and set aside. Add the tomato juice and bay leaves to the skillet. Cook, stirring, until slightly thickened, about 2 minutes.
Add the clam juice and 1/4 teaspoon salt and cook until the liquid evaporates slightly, about 2 minutes. Add the crushed tomatoes and bring to a boil over medium heat. Reduce the heat to medium low and simmer until the sauce thickens slightly, about 12 minutes.
Increase the heat to high. Remove the bay leaves and add the mussels to the sauce. Cover and cook until the mussels open, about 5 minutes. (Discard any unopened mussels.) Add the spaghetti and parsley; toss to coat. Season with salt and drizzle with more olive oil.