No, the president does not have to swear the oath of office on a Bible
Article II of the U.S. Constitution requires the president to swear an oath of office before taking on the role of president. The Constitution does not specify how this oath should be administered, according to the National Archives.
The only requirement for the oath comes from the 20th Amendment, which says the oath must take place at noon on Jan. 20th at the start of a term. Neither the Constitution or any of its amendments require any particular ceremonies or events to take place before a president can take office.
https://www.verifythis.com/article/news/verify/government-verify/trump-oath-bible-fact-check/536-f5ae683e-56d2-4e75-a82b-0e16dc29e6dd
>Again you have heard that it was said to those of old, ‘You shall not swear falsely, but shall perform to the Lord what you have sworn.’ But I say to you, Do not take an oath at all, either by heaven, for it is the throne of God, or by the earth, for it is his footstool, or by Jerusalem, for it is the city of the great King. And do not take an oath by your head, for you cannot make one hair white or black. Let what you say be simply ‘Yes’ or ‘No’; anything more than this comes from evil.
~ Jesus