I don't care what kind of device you use for alerting pedestrians...bells, horns, a loud mouth, fireworks, etc...you should always be prepared for a pedestrian to act in an unpredictable manner and proceed accordingly. Yes, you should have applied the brakes but you should have slowed and waited until the (clueless) pedestrian figured out what you were planning doing. If she went left, then pass her on the right instead of going further around her on the left.
As to bells, I only have one bike with a bell. I've never found it to have any effect on how pedestrians move when I ring it. They will still more in every conceivable direction. As I said above, I wait until they sort themselves out before I pass.