The bells were not rung to warn the British. His ride wasn't about warning the British.
Sarah never said the bells were to warn the British, nor that Paul Revere's ride was to warn the British. She simply said that, when caught, Revere warned the British soldiers what was waiting for them. And she was correct. And she mentioned that as Paul Revere rode through the towns, the bells started ringing to wake up the colonists so they could ready themselves for the Regulars who were coming out of Boston.