Farming Blood Stone Shards

Solution 1:

Your best bet are the beast-like creatures known as Large Huntsmen. They can be found in the sewers and just outside Father Gascoigne's boss room. There are also 12 that you can find in Central Yharnam according to this source:

• 1x Central Yharnam, atop a flight of stairs to the right of the first Mob Bonfire.
• 1x Central Yharnam, behind some boxes near the plaza, on the left hand side when passing under the Great Bridge.
• 1x Central Yharnam, on the Great Bridge at the opposite end of Cleric Beast, hidden behind a statue.
• 1x Central Yharnam, on a ledge reached by stairs down from the Great Bridge, behind some sandbags at the far end.
• 1x Central Yharnam, on a ledge reached by stairs down from the Great Bridge, behind some boxes which also blocks a hidden sewer entrance.
• 1x Central Yharnam, on a corpse right before the shortcut gate back to the Central Yharnam Lamp.
• 1x Central Yharnam, in the way to the sewers, if you drop onto a beam instead of taking the ladder down.
• 1x Central Yharnam, in the watery level of the sewers, in a corner next to an ambushing corpse.
• 2x Central Yharnam, sewers entrance, in one of the rat holes on the ledge above the boats. First cut down the hanging corpse up at the top by exiting through the window before the sewers entrance.

The 12 above will get you close to 16 required to bring your weapon to +3 (the maximum you can raise it with bloodstone shards), but you'll see low returns from drops and more likely out-level the area before you get enough. Future zones offer better farming opportunities and you can even unlock them for purchase using blood echoes or insight after certain events.