Bright Sheng might not be the first person a ballet company would think of when contemplating the creation of a composer’s residency. (He’s never written a ballet score, or expressed any interest in doing so.) On the other hand, New York City Ballet is hardly the first arts organization you might assume would be in a position to strike a major, multi-year deal with one of the preeminent composers of the era. (Ballet companies are not exactly rolling in money these days.) But Sheng is enthusiastically embracing his newest task, commuting to New York from his home in Michigan nearly every week, and getting involved in fundraising and education as well as the artistic side of the organization.