The culture around this varies a lot. I'm in Melbourne, Australia. Virtually all bike paths are "shared", and many have signs telling you to ring your bell when approaching pedestrians - you're not telling them to move out of the way, you're telling them that you're there.
In practice, I tend to use one ding to mean "I'm here" and multiple dings to mean "you're on the wrong side of the path and need to move".
But in no situation do I rely on a bike bell to avoid an accident.