Who is the antagonist?

The true antagonist in this story, according to the lawyer who narrates it, is not Bartleby, but the hopelessness that arises from failed communication. At the end of the saga, the lawyer reveals a rumor he has heard that Bartleby was previously employed in the dead letter office in Washington D.C, where letters that never arrived at their destinations are sent to be burned. This gives the lawyer a flash of insight into Bartleby's melancholy nature:

Dead letters! does it not sound like dead men? Conceive a man by nature and misfortune prone to a pallid hopelessness, can any business seem more fitted to heighten it than that of continually handling these dead letters, and assorting them for the flames?

This ending sheds light on to Bartleby's seemingly inexplicable desire to prefer not to do any work at all. If all effort is futile, if all words are doomed to perish unread, why would a scrivener—a copier of words—continue to make an effort?
The lawyer is a rare sensitive soul who shows compassion for Bartleby and tries to understand him, even if, in the end, he can not keep him in his employ.

Bartleby is the antagonist to the old lawyer, the protagonist who tells the tale. At first, Bartleby is a hardworking, conscientious employee, almost a model worker. But after a while he just stops working. In fact, he stops doing anything. In most cases, the antagonist is a character who actively does something to antagonize others, but that's not the case here. Bartleby is an antagonist without doing anything at all. And his passivity and inertia make him a particularly effective antagonist because it's very difficult to counter inaction with action. In telling his story, the lawyer admits that he's met some strange individuals in his time but none like Bartleby. He is so mysterious, so utterly inscrutable, that it's virtually impossible to deal with him. In the end, only drastic measures will do, and even then Bartleby remains every bit as much of an antagonist in the confines of a prison cell as he was in the office.