Slang: One year in prison.
Frequent viewers of cop shows like NYPD Blue or Law & Order will no doubt have heard this term used in context. For instance, Detective Lennie Briscoe might say after eliminating a potential suspect: "It can't be him, he's doing a bullet at Rikers."
Sources are silent on the origin of the term, since it isn't obvious how a year might be likened to a "bullet." Especially when you consider that a real bullet can earn its owner a great deal more than a year in prison, depending on what it hits.
Sources: www.convictsandcops.com, dictionary.prisonwall.org.