The significance of the Battle of Bunker Hill was that it showed the determination of the outnumbered American forces. Although the colonial forces were defeated their ability to inflict damages and heavy losses on the British was an important factor in increasing the support for the colonists military efforts.
"Why should we follow British rule?"
If you are talking about the tax collector from Britain that goes to tax the colonists, then he gets harmed. The colonists channel their anger through the tax collector to the government of Britain. They pour a sticky liquid on him and cover him in feathers.
What is your actual question?
