If heart is hit by a bullet...would you die instantly?

There are instances of gunshot wounds to the heart which have not been fatal - depends on the amount and nature of the damage done by the projectile. Given that "death" generally is defined as irreversible termination of brain function, whether or not accompanied by further systems failure, a death from a catastrophic heart wound alone would follow by a period of up to a few minutes from the time of the wound; brain activity will continue, briefly, in the absence of blood flow. Just ask any hunter who's had to track a well-shot (through the heart & both lungs) game critter into a bog or thicket.

More precisely, in the absence of blood, electrophysiological brain activity will continue briefly. The time or moment of death ( clinically ) is determined by the time at which the
ionic pumps that control flux across cell membranes have run down.

In sniper school they discuss the most sure way to garauntee the person dies is the center of the forehead.

it's the quickest and best way to shut down the brain and therefore all body functions.

I think iot depends on where in the heart the bullet pierces.

Why not take as an example the circumstance of the recent death of Steve Irwin's (Aussie zookkeeper). A sting ray's barb pierced his heart and as he pulled the barb out, he almost instantly died of heart failure. The barb could, without much imagination, been a simulation of a bullet.