You need some background in electricity before you can understand this answer.
The current running on the power line is in an electrical circuit . A generator has two wires: one provides the energy and carries the high voltage, and the circuit closes going back to the ground where the other end of the generator is.
In order for the bird to have current going through it, it should have a second connection to close a circuit through its body. As it is sitting at one point it does not feel much, although there should be some ionisation of the air for very high voltage.For large birds it can happen that if a wing touches a second power line, the bird not only fries, but can set fire to a forest.
A person on the ground touching a power line closes a circuit to the ground, which is a universal point for the return of the current.Thus, feels the shock due to the current running through him/her.