In the most advanced testing, bear biologist Tom Smith jingled bear bells in varying volumes in front of brown bears in Katmai National Park. Regardless of how vigorously he shook, 15 different sets of bruins ignored the bells. And yet they snapped at attention the second he broke a pencil in half.
This isn't 100-percent proof that bears don't respond to bear bells; Katmai bears are known for being relatively non-aggressive. But it means that in this specific case, the bells failed to warn and change behavior as intended.