In my opinion, the safest, fastest way to acquire blood vials at this point in the game is to buy them, even though they cost 720 echoes each after fighting Rom.
Many of the blood vial farming runs suggested online are quite good, netting 15-20 vials per run; however, if you aren't careful, they'll net you much less than that, as you'll have to use some to survive against the more difficult enemies (e.g. Hemwick executioners, giant hogs, scourge beasts). You can avoid this issue by farming for echoes in a safer, more predictable environment, then buying blood vials with the echoes you've earned.
The first floor of the Lecture Building is a great blood echo farm, consisting only of Slime Scholars (a relatively non-threatening enemy), and the run will net you around 13K-15K echoes -- enough to buy 18-20 vials. The Slime Scholars also have a chance to drop Quicksilver Bullets and Sedatives, both of which are nice to have in large quantities.
To summarize, I suggest farming the first floor of the Lecture Building for blood echoes to buy vials, because:
- The run is much safer than most blood vial farming runs
- The run takes around the same amount of time to complete as a blood vial farming run
- The blood echoes you get allow you to purchase a number of blood vials comparable to that of a blood vial farming run
I understand that this technically doesn't answer the question of "Where is the best location to farm blood vials?", but it does help the asker with their stated issue, and the end result is the same.