Can Bloodrush be countered with an instant that destroys attacking creature?
The blood rush card fizzles and goes to the graveyard.

To answer the question in the title: Yes.

Your understanding is correct. Since your Wring Flesh is on the stack above the bloodrush card, then it happens before the bloodrush is applied. 

Since the card's bloodrush ability was activated, it is discarded. The first part of the bloodrush ability says the card is to be discarded.