As @JLeslie points out, in the USA you can affirm rather than swear. Swearing on the Bible or in any other Christian context is rather foolish, since the Bible specifically says not to do so. Matt 5:33–36 quotes Jesus as saying, “Again, ye have heard that it hath been said by them of old time, Thou shalt not forswear thyself, but shalt perform unto the Lord thine oaths. But I say unto you, Swear not at all; neither by heaven; for it is God’s throne: Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King. Nor should you swear by your head, because you cannot make one hair white or black. But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil.”
So by swearing on the Bible, we are proving we either don’t know what’s in it, or don’t give a damn. In either case, we are proving our oath is meaningless.