"you" does not necessarily mean the one person that you are talking about. In fact, the original usage of "you" was always plural, which is why we say stuff like "you are" when using singular you, even though "are" is plural.
In this case, you're using "you" to mean not the specific person, but the office. This is normal, casual English. As long as you're not emphasizing the "you", like "How late are YOU open for?", it is understood from context that you don't just mean that person. (Emphasizing the "you", though, would make it a personal you and not a general one, by shifting the focus to be on the person you're talking to.)
So, yes - your phrase is perfectly fine in casual English. However, I will note that the phrasing "being open" to me, at least, would indicate more something like a restaurant or store, rather than an office. Offices aren't generally just open for people to walk in, so if anything was odd about your sentence, it would be that. Personally, I'd use something more like "Excuse me, what are your working hours here?" or "What's the latest I can get an appointment?". But you'll be understood if you ask how late they're open.