I'm writing this story... how does this expression I've used sound?

No, I wouldn't use that term myself. It gives an amusing tone to a very serious scene. It's like the bullet went on a journey to the victim's head, and when it arrived, it said "hi".

The second one isn't much better. Bullets don't run. They streak through the air, or fly, but they don't run, and they have no emotion. Don't overthink what the bullet did before it hit its target. The main thing is the effect thereafter.

Stupid.

The sentence works fine, for now. At any rate, move on and clean up later.

Atrocious.

Not the words I'd have chosen.

Your update implies you are writing a farce. If you are not, go with old prof

Let's go Hemingway-esqe. Bang and he was dead.

It sounds like a sentence in a book.

lame...it sounds lame. "greeting" sounds like a happy event. I doubt being shot in the head is a very happy event. You need to be more ominous, more graphic. Try...

The bullet traveled twenty feet before smashing the target's head.

The bullet traveled twenty feet before exploding the target's head.

The bullet traveled twenty feet before pulverizing the target's head.

The bullet traveled twenty feet before grazing the target's head. (in case the target didn't get totally wiped out by the bullet)

Like you're a psycho.