It's really not. These bells aren't that loud, you really only hear them once the cyclist is maybe 50 yards away. It's an incredibly important safety feature on low-visibility singletracks.
The only - very few - occasions when this tactic did not work were usually hikers coming in the opposite direction and being actively hostile. There was an angry lady once who refused to move even an inch to the right, so I had to move to her left, which was a large field of nettle... To this day I don't know what her problem was, but this happens sometimes.
Or maybe the question is: in retrospect do you have any wishes or regrets about how you handled it? Did you think of anything you should have done differently to defuse the situation? Do you have any strategies for avoiding or resolving the rare but possible next hostile confrontation?
Multiple times in the past I have goofed and reacted to someone’s aggression with return fire, and I don’t think it’s ever made anything better, usually it’s worse. I would like to have some prepared strategies in my mind for handling it smoothly.
Hikers and animals (dogs and horses) have right of way over bikes at all times on the trails I ride, is that true for you too? I’ve bumped into an angry hiker or two also, but on the whole they’re almost always super friendly and contentious. For me it’s more common than not that hikers are apologizing and getting off the trail before I even have a chance to yield, sometimes so much so that I feel bad about it. Anyway, I think we should take stock of all the nice hikers and lucky interactions, because it’s perfectly okay and reasonable for a hiker on a shared trail to not expect to yield. It’s definitely unkind if they refuse to make any room to pass, you do sound very patient, and the angry hiker experience totally sucks - triply if you got nettle all over. But at the same time, if we as bikers aren’t yielding first as much as we can, it’ll only get less fun for everyone and we can lose trails, right?