Bring a large pot of salted water to a boil. Add tortellini and cook 3 minutes; add beans and continue cooking until tortellini is tender, about 5 minutes. Drain; rinse under cool water. Drain well. Place in serving bowl. Stir in onion, olives and tomatoes.
In a small jar or plastic container with tight-fitting lid, combine oil and garlic. Let stand 10 minutes, then add both vinegars, basil, oregano, salt and pepper. Shake well. Stir half into tortellini salad.
Cover salad with plastic wrap and refrigerate up to 1 day. Remove from refrigerator 30 minutes before serving; stir in remaining dressing if needed.
