I am exercising at Kung Fu's dojo and wonder whether kneeling and bowing down is an idolatry (Avodah Zarah)? The floor has soft mats. The reason explained to me is that it's done as a form of greeting to a person. In general, the gesture recognizes that you are submitting and giving respect to the person to whom you are bowing, as at that moment they could cut your head off!
Bowing in Kung-Fu will take various different forms; not surprising as there are hundreds, if not thousands, of individual styles from various families and various regions all throughout China.
In China, bowing (especially the traditional kowtow) serves as a sign of reverence. Modernly (following Imperialisms decline in China), the kowtow has been replaced by the standing bow in many formal situations. Bowing is also common under Buddhist traditions, especially when honoring both the student-teacher relationship, as well as in honoring ancestors and memories of predecessors.
Finally, bows may be used in apology. As @BenCole said in one of his comments to the original question, this may be a way of bearing the neck in a sign of supplication, but is commonly used by political and celebrity figures to show remorse for a perceived fault.
Bows in Chinese martial arts tend not to be as strict as bows in Japanese martial arts, as bowing is not such a formalized practice in China any longer. The core ties are, however, to both Buddhist and Confucian traditions.