They affirm they will tell the truth, consonant with the US Constitution. Forcing an atheist to swera on the Bible would be a constitutional no no.
Federal courts have never required the use of a Bible or the words "so help me God." The U.S. Constitution, every time it mentions oaths, always says "oath or affirmation." This was because, even then, there were a lot of religious dissenters (Quakers, and probably some others)who wouldn't swear on a Bible.
Today, federal law is that the witness can pretty much use any form of oath or affirmation he wants, as long as it is clear that (a) he is promising to tell the truth, and (b) he understands that he can be convicted of perjury if he lies. (The same is true in the state courts I have been in, but I have never been in a North Carolina state court, so I don't know if they really make everyone swear on a Bible.)