How does the potential of a bird increases after sitting on a wire due to which, it does not get electric current?

Current is the result of a difference in electric potential between two points.If an entire object is at the same potential, then there's no reason for current to flow anywhere over, under, around, or through it.  That's how an electric-repair lineman goes up in an insulated bucket, connects himself and the bucket to the line, and then proceeds to work on the live line without danger.The difference in electrical potential across the entire bird is the differencebetween his feet ... perhaps 1 to 10 inches along the length of the line that'shundreds of yards or hundreds of miles long.  The potential difference   between those two points a few inches apart is very small.