Maybe in 6 cases out of 10 a gentle bell ring works fine where I ride (100% mixed paths, where the law requires everybody to stay right). The remaining 4 are ugly scenes to watch. Sometimes pedestrians get over-cautious as swekarl described, although here they don't just run, they hurl abuse at you as well.
Sometimes, upon hearing the bell, a group of pedestrians quickly reorganizes, everybody moving this way or the other, finally leaving the path as blocked as it was to begin with. And then there are those who leave a narrow gap for other people. When they hear the bell, they get scared, apparently deciding that the gap wasn't wide enough and promptly move to block it. I've had this happening to me so many times that I now try to pass through the gap in stealth mode, if possible.
In a really close-call situation a badly aligned front brake is better than any bell. A loud screeching sound approaching leaves nobody in doubt. They move out of way first, then look around for the source. With bell it seems to be the opposite.
And how about dogs? Do you have people walking their dog(s) in a 3-meter leash on mixed paths?
--J