The result of Battle of Bunker Hill was A. an unqualified British victory. Even though they won the battle, they suffered a massive loss in their troops, and therefore the Colonies gained encouragement for the remaining battles.
The british won the battle but unqualified because the Americans were REKTING the british. Don't get me wrong though. The Americans were low on ammunition and their generals said this famous quote: "Don't fire until you see the whites of their eyes!" That was a good call though because that's how many British soldiers lost their lives. When the Americans ran out of ammo they left the base to the British.