You're correct: the vampires have regenerative abilities and thereby would are essentially able to be immortal, so long as they don't starve to death, get their head destroyed, or get too much exposure to ultra-violet light. Their structured, hierarchical society lived for a very, very long time underground.
During the prequel light novel Owari no Seraph: Ichinose Guren, 16sai no Hametsu, which opens about 10 years prior to when the virus strikes, the vampires were not yet rampant above the surface of the Earth.
The reason they decided to emerge was when the Four Horsemen of John (a.k.a. Horsemen of the Apocalypse) surprisingly arrived in 2012 and started killing humans. The Owari no Seraph Wiki says,
In response, vampires came into the open and saved as many humans as they could as human livestock out of concern for their drastically diminished food supply.
It is likely that, until that point, vampires preferred to covert travel above ground to snatch individual human prey without alerting humankind to their existence (during that period, it's very reasonable to assume that once in a while a human got tipped off about the existence of a vampire, but it was never accepted as fact by human society at large [chalked up to the level of a report of monsters, ghosts, or UFOs]), but once the humans started dying off at a rapid rate, the vampires reasoned that they could not continue their subtle hunter/gatherer style and needed to turn humans into livestock (a farming style that they could control themselves).
