Melville's title itself, "Bartleby the Scrivener: A Tale of Wall Street" indicates the significance of the setting as well as characterizing it. For, the lawyers chambers look upon a white wall of the interior of a spacious sky-light shaft and a lofty brick wall, while the other chambers have little if no views. Bartleby works in a corner by the folding doors behind a screen and has a window that "commanded at present no view at all. After Bartleby works under these conditions for some time, he begins to say "I would prefer not to" when asked by his employer to perform certain tasks. Eventually, the "inscrtable scrivener" retreats whenever possible "into his hermitage" of folding wall and viewless window.
Even when the lawyer moves to another office and the screen is folded leaving him the "motionless occupant of a naked room," Bartleby does not move. He haunts the building until he is taken the the Halls of Justice. There at the prison, Bartleby merely stands facing a high wall; he loses all will to live and dies, huddled against a wall where the lawyer discovers him with his eyes open. The walls that have closed Bartleby from human contact and from seeing nature outside have deprived him of one of man's most basic needs, that of companionship. Sadly, Bartleby accepts this isolation, even "prefering" it. But, it kills him. After his death, the lawyer learns that Bartleby had worked in the Dead Letter Office at Washington, from which "he had been suddenly removed by a change in administration." There, too, he was isolated.
The walls around Bartleby--his environment--affect him greatly, reducing him to a passive man. This desolation in Bartleby even begins to affect the other men who start to use his word prefer, and it affects the lawyer who himself becomes passive about ridding himself of Bartleby. As the walls close in on Bartleby, he retreats into himself more and more until, in his isolation behind walls, he dies, tragically huddled at the base of a wall.
Melville's subtitle "A Story of Wall Street" conveys the distant and often conflicting relationships between employers and employees that occurred in his time. In a way, Bartleby becomes symbolic of the growing distance in the late 1800s between employer and employee; as he is set apart by folding walls and viewles windows, his depersonalization occurs a result of this isolation; he is the estranged worker in an uncaring system. A thesis for Melville's story could establish the relationship between the walling out of Bartleby from his employer and his passive resistance and eventual retreat.
This is a really long short story, and the setting is consistent throughout the work. It is a law office in New York, presumably Wall Street (as noted in the original subtitle). In this office are men who know virtually nothing about each other--except for a few eccentricities--despite the fact that they're trapped in this office together for long, tedious days. Their surroundings are impersonal, matching the impersonal nature of both their relationships and their work.
Melville is clearly commenting on the impersonal nature of business--which is why the characterizations and interactions are impersonal and somewhat isolated. We know that Turkey and Nippers have issues with alcohol (and between them make one decent full-time worker) and that Ginger Nut is a young boy who is supposed to be learning the law but in reality just runs errands--particularly the acquisition of ginger nut cookies--for the others. We know very little about the narrator, and we know Bartleby would "prefer not to." That's about all we'll ever know despite their close proximity and their common working relationship.
This is an interesting question, because anyone who remembers reading this story probably only thinks about Bartleby and his famous refusals. The setting, though, is perfectly suited to the theme. Any thesis using the idea of "impersonal" or "business only" or "isolation" would be appropriate, it seems to me.
In "Bartleby the Scrivener" the setting is a dull office with nothing but the barest of furnishings. The setting never changes. The significance is that it is very impersonal. There is nothing of the people who work there in the office. No personality. Like Bartleby.