Drain the beans and place in a large, heavy saucepan over medium heat with the chopped carrot and celery. Add 2 cups fresh water and bring to a boil, then reduce to a simmer, cover the pot, and cook until beans are tender, about 45 minutes to 1 hour. Check water level from time to time and add boiling water as it cooks down so that beans are always covered. When tender, drain, place in a bowl and set aside.
Place mussels in a large pan with the wine and set over high heat. Cook, stirring frequently, until all the mussels have opened. Remove from heat and set aside to cool. Strain cooking liquid through several layers of cheesecloth into a small bowl and set aside.
When mussels are cool enough to handle, remove flesh and discard shells.
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a saucepan, heat olive oil over medium-high heat and add garlic. When garlic is soft but not brown, add tomatoes and cook for 10 minutes, or until tomatoes are soft and disintegrating. Stir in cooked beans and simmer gently while pasta cooks.
Cook pasta in boiling water until it is almost cooked through, about 8 minutes. Drain the pasta and add to the bean mixture. Add the mussels and strained mussel liquid. Stir over low heat 5 minutes, then add parsley, basil, and salt and pepper, to taste. Serve immediately.