I'm assuming you are a U.S. Citizen, and that you have a valid Visa. From http://travel.state.gov/foreignentryreqs.html

CHINA, PEOPLE’S REPUBLIC OF - *Passport and visa required. Transit visa required for any stop (even if you do not exit the plane or train) in China. Business travelers are required to obtain formal invitation from Chinese business contact. Tourist visas are issued only after receipt of a confirmation letter from a Chinese tour agency or letter of invitation from a relative in China.

If you have a Tourist Visa I would NOT recommend saying that the purpose of your trip is "Business". ("Pleasure" would be the best answer.) If on the other hand, you have a "Business" Visa then you should simply say that the purpose of your trip is "Business". (Sometimes I get questions like, "What Company do you work for?). The term "Mileage Run" might not mean much to the C&I official?