I don't think people think highly enough of bicycles for there to be a museum... Your best bet might be to visit Flying Pigeon in Tianjin, or Yongjiu/Forever in Shanghai. They might have displays of their older models, but I wouldn't expect much.
I was wrong. This article (in Chinese) talks about a Mr. An, who has a small bike museum (edit: must be very small: it's in his home) opposite the Worker's Cultural Palace in the Nankai district of Tianjin.