I think there's an inverse square law going on here.
Let's take a towpath as a good example because they are mostly shared paths of limited width, so the options are, well, limited.
The progress/escalation works something like this:
Two people walking with a dog.
At 30 meters away, (~10s?) you ring your bell.
a) They hear you, look around and can shuffle both ways before deciding to clear a path on the water side. Success.
b) They don't hear you.
At 15 meters away (~5s?) you ring your bell again
a) They hear you, you are now at least 4 times more likely that they will each shuffle the other way, with the dog completing a cat's (??) cradle of lead across the path, but there is still a chance they may clear the way. By now, you will have started to slow down
b) They don't hear you
At 7 meters away (~3s) you ring your bell again.
a) They hear you. Really? These two? They wouldn't hear a volcano unless you shoved it up their backsides, you know that already. Even if they do by this stage the odds are up to 16:1 that confusion will rule their placement. You are almost certain to have to (hushed tones) stop. Smile, excuse me!! and be on your way
There is no plan b