The world sort of is the story in Bloodborne, there's not nearly as much lore as there was in DS1 (though that's mostly because there are fewer areas / items with unique descriptions).

The story is thus (potential spoilers ahead, but only up to the LP): There is a schism, at some point, between the scholars of Byrgenwerth and the progenitors of the Healing Church, namely Provost Willem and Laurence, the two dudes in the cutscene after Vicar Amelia talking about the old blood and whatnot. Laurence discovers the healing properties of blood and sought communion with the Great Ones, going on to found the Church, but Willem thinks this is dangerous and seeks to make contact without the use of blood. He believes that the human mind is too fragile, and that, literally, they need "more eyes" in order to ascend and become kin of the cosmos. This is why all the shit you find in Byrgenwerth uses slugs, or phantasms, as a medium for spells instead of blood, and also why all the enemies around the area (and Rom!) are covered in eyes. There are other factors in play and other schools of thought related to these two but Laurence and Willem are the main players at this point.

It's also around this point in time that the red moon draws near and weird shit starts to happen. Look back at these lore notes with the context we have now (and will probably have more tomorrow, provided they go for progression and not the Cathedral hunter) and it starts to come together:

"Madmen toil surreptitiously in rituals to beckon the moon. Uncover their secrets."

"Nightmarish rituals crave a newborn. Find one, and silence its harrowing cry."

"When the red moon hangs low, the line between man and beast is blurred. And when the Great Ones descend, a womb will be blessed with child."

It's around the time you enter Byrgenwerth and face Rom that the games takes a serious nosedive into cosmic horror territory. This game has a pretty major (and very intentional) genre whiplash and so most of the lorestuff is loaded at the end after the major reveals happen and serve to recontextualize everything we've seen so far.