Bell collars aren't really very effective, unfortunately. Cats generally hunt by staying still and quiet and waiting for unsuspecting prey to happen upon them, then pouncing on it when it does. So by the time the bell is ringing, it's already too late for the poor critter.

Source: have cat with bell collar that was formerly allowed into a small fenced-off area next to the house, and it had no trouble murdering quite a number of different creatures even under those constraints.