In Herman Melville's "Bartleby the Scrivener," the narrator shows apathy toward Bartleby in a number of ways, although I find the narrator's most remarkable example of apathy to be his passive aggressive refusal to take any real action in forcing Bartleby to leave. He does, of course, tell Bartleby to leave on several occasions. However, he never actually takes any direct action in forcing Bartleby out of the offices. Indeed, rather than calling the police to force Bartleby off the premises, the narrator decides to move his business to a new location in order to escape Bartleby. This process, which is undoubtedly time-consuming, costly, and generally arduous, is an absurd excuse for the narrator to avoid dealing with Bartleby. While this isn't apathetic in the lethargic sense of the word, it is apathetic in the sense that the narrator is refusing to actually take decisive action and attack his problem at the source.
However, if the narrator is somewhat apathetic toward Bartleby, then he's also empathetic. Indeed, if the narrator doesn't actively lay hands on Bartleby and throw him into the street, it's because the narrator feels sorry for the man he employs. Upon closely observing Bartleby's radically isolated existence, the narrator observes "he seemed alone, absolutely alone in the universe. A bit of wreck in the mid Atlantic." You can read this passage in its full context using eNotes' excellent online version of the text but, for now, what you need to know is that this passage exemplifies how sorry the narrator feels for Bartleby, and how he tries to understand the strange man's lonely existence. As such, if the narrator's apathy prevents him from throwing Bartleby out once and for all, then so does his empathy.