Birds don't get shocked on power lines because they do not make a complete circuit path for the electricity; they only have one point of contact with the circuit rather than two points. However, birds can be shocked and electrocuted on power lines if they extend their leg or their wing and touch another wire.
The bird is shocked and electrocuted because it has created two points of contact with the electricity and the electrons will now move through the body of the bird. Another way that the bird could be shocked and electrocuted would be if the bird touched the wood pole that holds the wires. This wood pole is buried underground, and so touching it would open up the bird to two connection points and lead to electrical shock.
The electrical current in the wires is really a "movement of electrons" ; therefore, the electrons are moving from the ground to the power lines, into the TV or phone in a person's home and then back to the power lines and to the ground. This is what is known as a closed circuit loop. Creating one point of contact with the circuit, which is what the birds do, does not give the electrons any reason to travel through the bird because there are no moving electrons within the bird.