Sympathy with characters is one way of reacting to a work of fiction, but it is not either the only way of reacting nor are all stories designed to elicit such reactions. In this case, the character of Bartleby, as presented through the lens of the affable but not profound narrator, appears more of a mysterious and enigmatic character that serves as a litmus test of the reactions of others than a fully-rounded character. While I find the relationship of the narrator to his employees interesting, and appreciate Melville's artistry in making the narrator's fascination with Bartleby credible, the story to me seems designed to evoke reflection rather than empathy.
The narrator appears a basically morally good character and good boss. He allows for the foibles of others, and goes out of the way to treat his employees well. His style of management is paternalistic, and while he acts out of self-interest, he is also generally benevolent.
Personally, as an employer, I probably would have replaced Bartleby much earlier, rather than tolerating him for so long and moving offices to avoid him.