The same bird on the tree has more gravitational potential energy. This is because it is at a higher distance from the ground as it is on the tree, than when it is on the ground.
Considering also the formula for Gravitational Potential Energy GPE = mgh
For the bird on the ground, h =0, therefore GPE = m*9.8*0 = 0
For that on the tree = mgh = m*9.8*h
Of course the one on the tree has a value greater than zero.