Herman Melville was writing for the educated elite literary audience of his day. These were the individuals who had a sound background in classics and a compelling interest in political affairs of their day. The short story "Bartleby the Scrivener: A Tale of Wall Street" was first published in Putnam's Magazine in 1853. Putnam's is described as having been a monthly magazine of "American literature, science, art, and national affairs, published by G. P. Putnam's Sons." Putnam's Magazine's first edition appeared in 1853, the same year that "Bartleby the Scrivener" was first published. Putnam's ran until 1857, then, after an hiatus, reappeared in 1868 and ran until 1870. Apparently, it never met with the success of some other American publications. Nonetheless, the reading audience of Putnam's Magazine was the upper crust of American society who would have had personal experience with lawyers and on Wall Street.
It is interesting to note that Putnam's Magazine is archived at Cornell University, with archived issues availbale online through Cornell University Library.
It would seem, initially, that Melville was writing for an existentialist or maybe even nihilistic audience. But that would be too simple and it predates most of the more famous existential thinkers (Camus, Sartre), with the exception of Kierkegaard who lived during the 1st half of the 19th century. But one thing about "Bartleby" is its ambiguity, so it could have been written for psychologists, philosophers, religious scholars, sociologists or other academics. Most likely, Melville was also writing this for the everyday worker. The story does seem like a satire of passivity, nonconformity and the mind-numbing quality of many occupations. One of the links below talks about the approach of the Civil War and how the North despised slavery while the Southern politicians claimed the life of the Northern wage (factory) worker is akin to slave labor. So, Melville could also have been writing this satire for the worker as well as the politicians. Anything, or all of these, are possible. I don't know a lot about Melville's biographical info, so I don't know about his politics. But I did read that philosophers William Priestly, Ralph Waldo Emerson and Arthur Schopenauer may have been influences here. This is in reference to their ideas about self-reliance, free will, and that the individual must isolate him/herself from society in order to completely avoid conformity and passivity. In the end, this story is written for everyone who feels stuck in a mind-numbing job or everyday life. Maybe we can only speculate about what Melville had in mind. This story always reminds me of the movie Office Space.