How deep underground would a bunker need to be in order to escape effects of a nuclear blast?

It depends on the source of the nuclear blast. A hydrogen bomb can be made to release any amount of energy it's makers desire - it just depends on how big they build it. If they worked hard and long enough, they could make a hydrogen bomb big enough to vaporize the planet, in which case you could dig all the way to China and it wouldn't make a bit of difference.