Ed
If the President Elect chooses to swear his oath on bible - he does so because he chooses to. Unless there is a law that I'm not aware of the oath or affirmation that he states is governed by the constitution.
Article 2 Section 1 states the following:
Before he enter on the Execution of his Office, he shall take the following Oath or Affirmation:--"I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States." It says nothing about a bible. Freedom of expression.