I know an answer has already been accepted, but i think this could fit as well (please go easy on me, this is my first answer):
are the members of the gang paper, scissor and rock?
Of us there are three
they are indeed three
one of which is part tree
Paper comes from trees
The other one you should not fear, but it will make you burst in tears
There's no actual reason to fear a pair of scissors, but you could hurt your self pretty badly with it
As for the last one, and there is no bluffing, that's the one you'll never see coming
Not really sure about this and this is really streched, but it kinda remids me of Harry Potter when Harry hits himself with a rock to alert himself of the people coming to hagrid's place (Harry Potter and the prisoner of Azkaban)