Ok so the funniest thing happened to me, not sure if this is a bug or not.
I was on Hunter's Nightmare on the Old Hunter's DLC, going through the dark cave where the Amygdalan Arm supposed to be, fought the hunter with the gatling gun inside the cave, beat him and proceed to accidentaly agrroed the BSB guarding the Amygdalan Arm.
Since i dont have enough blood vial i decided to just back away but i noticed that the BSB slowly catching up to me and it followed me until the blood river area, it even fought with every remaining bloodsucking beast on that area that i didnt kill and they did a good job shaving the BSB's HP to about 2/5
After all that it followed me again, walking slowly, as i backed away also slowly, getting past Simon the NPC, and finally through the shortcut to the Cathedral Lamp which couldnt fit the BSB, so i used multiple charged attack with my Ludwig's Holy Blade and killed it in safety. EZ!