Good evening dear hunters, Hereticalthoughts here to bring to light a few bits of information that may be interesting regarding the standard ammunition of our trusty firearms, the quicksilver bullets. Keep in mind that the information may or may not really be all that relevant within the world of Bloodborne itself, but I certainly found the potential references intriguing.
Now, a lot of you likely know that the term quicksilver is something of a nickname or slang term for mercury, a metal most known for it's liquid state at room temperature. Unless it's treated somehow (the simplest method known to myself is to expose it to extreme temperatures) it will remain in liquid form. This leads to the first tidbit, as it's clear that within the Bloodborne universe there is a lot of alchemy and science going on behind the scenes, and it's possible that the source of these odd rounds may come from a rather wealthy organization like the Church of Healing referenced by multiple characters in the game.
The second tidbit is simpler, many of the beasts the player encounters (and indeed a few humanoid enemies) are rather dog or wolf like in demeanor, the most obvious examples being the werewolf like enemies. In most fables concerning lycanthrope like monsters, silver is considered to be the means of killing them, mostly through silver bullets. Of course mercury and silver are definitely different metals, but still it's clear that it's a reference in my book.
Finally, mercury was pretty popular in the 16 through 17 hundreds, a lot of trades and even medical practices involved mercury in one form or another. However, mercury is toxic to humans, and many people suffered greatly for applying it in an ignorant manner (such as by inhaling mercury fumes, or from getting it into their blood stream, etc.), considering that quicksilver rounds are used by the hunter so much, and one of the more popular symptoms of long term exposure to mercury is mental instability such as the violent and obsessive behaviors of Yharnam's residents, it's almost certainly a throwback.
Feel free to point out or correct anything I've missed or didn't state, as I'm no expert on mercury and of course Bloodborne hasn't been played to the point that information is easy to get yet.
May the good blood guide you!