Does Bloodborne exist in the same universe as the Dark Souls games?
Hidetaka Miyazaki has stated several times that Bloodborne is a new game and has no link to either the Dark Souls series or the Demon's Souls series. Series which are not connected either (see this question).
This was never considered as a Demon’s Souls II (source)
The easter eggs have to be considered as "fan service".
An interesting analogy I found on GameFaqs, illustrating the fact that although two games might look a lot alike, they are not necessarily related : "Are Grand Theft Auto and Red Dead Redemption part of the same series?"