The size of the voltage in the wire is not what determines the current through the bird. It is the difference in the voltage between the bird's feet. If the wire is charged by a 600V source, the voltage between the birds legs is not 600V. The actual voltage difference is very small. The birds legs are touching two points very close to each other on the wire. The 600V drop is over the entire length of the wire from the power source back to the power source. The bird would have to be touch parts of the wire miles apart in order to feel any significant amount of voltage. The electrical wire is also a good conductor, which means its resistance is small and so the voltage drops only a small amount over any distance that a single animal could reach.

To be more concrete, say you hook up a 9V battery to a light bulb with two wires. The wire connected to the positive terminal will be at a voltage of 9V. The entire wire will have a voltage of 9V. This means that, if you connect a pair of voltmeter probes to the same wire, you will measure a potential difference of zero, because both probes will be measuring the same potential. It is only when the probes are in contact with different wires that you will measure the 9V difference.

Remember, it is differences in voltage that cause current, not just an amount of voltage. I can be perfectly safe standing in a 600-foot tower. I am only in danger if I fall from that tower and hit the ground 600 feet below. If the bird on the wire could somehow reach the ground or another wire at a different voltage at the same time, then it would feel the full 600V potential difference, because two parts of its body would be feeling different voltages, which would cause a current to flow.

Your parallel circuit works because the first resistor causes a large drop in electrical potential from one side to the other. So, when you connect a second resistor in parallel, there is a potential difference across the second resistor. The bird on a wire is more akin to this diagram:

The pluses indicate the constant higher voltage on the top wire and the negatives indicate the constant lower voltage on the bottom wire. It is only when a resistor straddles a positive-negative difference that a current flows through it. The bird resistor at top, with its legs touching parts of the wire with identical voltages, will have no current flowing through it. All of the current will flow through the much lower resistance wire.

The bird will have a resistance of, say, 1 M$\Omega$, while the wire between the birds feet will have a resistance of, say, 0.1 $\Omega$. Calculate the amount of current that will flow in the 1M$\Omega$ resistor in a parallel configuration.

The size of the voltage in the wire is not what determines the current through the bird. It is the difference in the voltage between the bird's feet. If the wire is connected to a 600V source, the voltage between the birds legs is not 600V. The actual voltage difference is very small. The birds legs are touching two points very close to each other on the wire. The 600V drop is over the entire length of the wire from the power source back to the power source. The bird would have to be touch parts of the wire miles apart in order to feel any significant amount of voltage. The electrical wire is also a good conductor, which means its resistance is small and so the voltage drops only a small amount over any distance that a single animal could reach.

To be more concrete, say you hook up a 9V battery to a light bulb with two wires. The wire connected to the positive terminal will be at a voltage of 9V. The entire wire will have a voltage of 9V. This means that, if you connect a pair of voltmeter probes to the same wire, you will measure a potential difference of zero, because both probes will be measuring the same potential. It is only when the probes are in contact with different wires that you will measure the 9V difference.

Remember, it is differences in voltage that cause current, not just an amount of voltage. I can be perfectly safe standing in a 600-foot tower. I am only in danger if I fall from that tower and hit the ground 600 feet below. If the bird on the wire could somehow reach the ground or another wire at a different voltage at the same time, then it would feel the full 600V potential difference, because two parts of its body would be feeling different voltages, which would cause a current to flow.

Your parallel circuit works because the first resistor causes a large drop in electrical potential from one side to the other. So, when you connect a second resistor in parallel, there is a potential difference across the second resistor. The bird on a wire is more akin to this diagram:

The pluses indicate the constant higher voltage on the top wire and the negatives indicate the constant lower voltage on the bottom wire. It is only when a resistor straddles a positive-negative difference that a current flows through it. The bird resistor at top, with its legs touching parts of the wire with identical voltages, will have no current flowing through it. All of the current will flow through the much lower resistance wire.

The bird will have a resistance of, say, 1 M$\Omega$, while the wire between the birds feet will have a resistance of, say, 0.1 $\Omega$. Calculate the amount of current that will flow in the 1M$\Omega$ resistor in a parallel configuration.