Cook the pasta in a pot of salted boiling water. Drain when the pasta is al dente and rinse pasta with cold water, shaking it around. Let it sit in a colander to drain thoroughly.
In the meantime, chop the peppers and artichoke hearts. Add them to a large bowl along with the olives, onion and bocconcini.
Add pasta to the bowl and mix well.
In a sealed container, combine all of the dressing ingredients and shake them up well to create a consistent emulsion.