Eastern societies bow a lot; it is a sign of greeting, courtesy, and respect; it does not mean that you are acknowledging that the person or thing being bowed to is a god. Some societies use the French style le bisou double cheek kiss to greet and show respect. In the military, we salute. In Western societies, we mostly use the handshake. Therefore, the bow, salute, and handshake are equivalent. If you shake hands with the Dalai Lama, are you worshiping him or merely greeting him and showing respect to him as a human being. Instead of shaking hands, if you greet him with a bow as used in his county, are you worshiping him. Is a police officer that calls a child rapist “sir” showing respect for the rapist’s behavior or merely showing respect toward another human being?
If you donate money to a charitable group that then gives the money to Buddhist temple to use in feeding the poor, are you worshiping Buddha? If you are touring a Buddhist temple in Japan and you bow as you enter the temple as is the tradition of the country you are in, are you worshiping Buddha. The Bible in Matthew 22:21 (King James Version), “They say unto him, Caesar's. Then saith he unto them, Render therefore unto Caesar the things which are Caesar's; and unto God the things that are God's.” When bowing, you are merely rendering unto the person or entity the respect due that person or entity. If in you heart you know you are only bowing as a sign of respect, are you judged by God as bowing in worship of another god? Christians believe that God knows what is in your heart, so He must know your true intentions.
In Exodus 23:24 (New International Version) the bible says “Do not bow down before their gods or worship them or follow their practices. You must demolish them and break their sacred stones to pieces.” Does this mean that, when the martial art class requires you to bow, you are required by God to rip all their religious symbols off the wall and destroy them?