Generally, cyclists and pedestrians shouldn't be sharing the same piece of infrastructure bar the few shared paths, crossing at junctions or on roads without footpaths.
On shared paths, cyclists need to travel at slow speeds so as to be able to react in time to avoid pedestrians wandering into their path. Some pedestrians here tend to take exception to cyclists ringing a bell, interpreting it as aggressive, but perhaps if it was more common it would become less of an issue.
On roads with no adjacent footpath on either side, pedestrians must travel on the right facing on-coming traffic, so there should be no need for a bell to warn of an oncoming cyclist if they are paying due care and attention.
In other cases, cyclists shouldn't be on footpaths, pedestrians shouldn't be on cycle lanes, pedestrians should look before they cross a cycle path or road, and cyclists should be prepared to stop when approaching pedestrian crossings. A cyclist, or any other category of road user shouldn't need to audibly alert others as they approach. Expecting them to do so absolves the pedestrians of their duty of care to behave in a responsible manner and not walk out in front of traffic without first checking it is safe to do so.
