Cook the pasta according to the package directions. Reserve 1/2 cup of the cooking water, drain the pasta, and set aside. Wipe out the pot.
Heat the oil in the pasta pot over medium heat. Add the bell peppers and garlic and cook, stirring occasionally, until the peppers are tender, 5 to 7 minutes.
Add the arugula, bocconcini, the cooked pasta, the reserved pasta water, 1 1/4 teaspoons salt, and 1/4 teaspoon pepper. Cook, stirring, until the arugula is just wilted, about 1 minute.