My question: At the very initial moment when the bird sits on the live wire, the bird and the live wire have a potential difference, which is normally of the magnitudes of $1000'$s. But why the current due to the charge build up build up doesn't kill the bird?
Okay, I have formulated my own theory for this. So please validate this too:
From google, the capacitance of human body is about $180pF-200pF$ and so birds should have a lesser value, since they are small. From this the charge build up in a human body would be(voltage of the live wire is $11kV$ in India)
$Q=180\times 10^{-12}\times 11000=0.00000198$
So such small charges cannot harm you.