Around where I ride, bells are mandatory equipment. Also, vocal calls ("on your left" or similar) are unheard of.
With that in mind, maybe a year ago I took a sample of 40 instances on my commute when I actually had to ring the bell. In 60% of cases pedestrians' reaction was positive or indifferent, 40% were negative. This is of course statistically solid, peer reviewed scientific research.

Overall, bell did seem to convey the message pretty well but for some reason, 40% of people found it annoying.
I've noticed I get the best response to noise that doesn't seem to be intentionally generated. I click my brake levers, or keep front brake pads poorly toed in so that they make noise when applied etc. Pedestrians think it was their accurate situational awareness that alerted them to the potential collision, instead of some annoying outside signal.
iDeaf people are a class of their own. Same with cell-phone blabbering owners towing their dogs in a 10 meter retractable leash. With those, there's no telling what will happen even if you do manage to get their attention in time.
--J