Here's a quick video I made of the glitch in the clinic that can yield a ton of blood echoes. Combined with the clinic skip (https://youtu.be/wzhsYPv9aUM) you can get as many blood echoes as you want at the very start of the game, prior to encountering your first boss.
Details in description, but the basic goal is to kill the dogs in their cages, then enter the clinic and drag the "magic" spot where you get the dog-ghosts echoes to the door by the lantern by forcing a few zone transitions. Eventually it will stick and you can quickly cross a line over and over very easily to get 2k in about a second.
In the video, I cut a section out where I was trying to pin down the sweet spot, but on a fresh character that proved unnecessary. In the back door, out the front, back to the NPC and then it sticks.
https://youtu.be/vZIFw6fEPkI
Let me know if it doesn't work for you and (if possible) what step I missed and I'll update the description for others. Possible steps include: triggering the echoes on the far side of the gurney closest to the door one or more times, and positioning the camera so you can see out the front of the clinic at some point while setting up the main spot.
Why do you get those echoes in the first place?