The bell tells Winnie when to sleep and when to wake. Fun, huh? It's not all that different to how our alarm clocks and school bells dictate what we do and when we do it—if only there were some kind of universal snooze button. How many of us live our days on autopilot without questioning why we do the things that we do? Perhaps the bell is meant to show us the crazy nature of Winnie's life, and ours as well.
The Bell could also represent God, and not that nice bearded old man in the clouds, but an angry hellfire-and-brimstone kind of God who wants us to believe that the world is meaningless and cold. Like Winnie, we go through experiences and moments, which "hurt… like a knife. A gouge" (2.1).
Some people might even think that the bell might function as a stand-in stage manager. Winnie is an actor playing a part on stage, and Beckett was a big fan of metatheatricality.