Some of our Presidents didn’t use the bible in their private ceremonies, only in public.

Teddy Roosevelt didn’t use it for his first term inauguration, Franklin Pierce didn’t swear but affirmed his oath, George Washington (and G.H.Bush) swore on the Masonic Bible (Masons = cult in many conservative Christian circles.)

That’s a rather checkered history about the use of the bible for swearing in the oaths of office. http://memory.loc.gov/ammem/pihtml/pibible.html