The tradition of using a Bible during the swearing-in goes back to the very first inauguration, but not all Presidents have used one.

There are so many traditions on Inauguration Day, but only one is required by law, and that is saying the Oath of Office. Taking the Oath with your hand on a book According to the U.S. Department of State,

Some presidents did not use a Bible to take the oath of office, including Theodore Roosevelt, who did not use anything when he was sworn into office in 1901, and John Quincy Adams, who chose a legal book for his 1825 swearing-in, to signify his responsibility to uphold the U.S. constitutional law.