How did the colonist react to the battle of bunker hill?

That battle was really significant because that battle was the first major "victory".

They "lost" because they lost the hill but they "won" because of the casualties they inflicted on the British. In that battle, only around 400 colonist died while there were over 1,00 casualties on the British side. This battle gave a large confidence boost which then created confidence with hope in the colonist.