What do you do?

Use hypnosis, attract, thunder wave, or torment? Or a masterball.

I would master ball that bitch.  Unless I only have one or no master balls.

I only encountered a shiny once in my life, and I didn't have any pokeballs with me :( It traumatized me for life, I kept checking my bag for balls, to no avail. Or I only had 1 or 2 left, which failed, I do know I didn't caught it.

 I would use an ultra ball, great ball, pokeball, master ball or anything I have on the bag...

You only ever get one...

Quick Ball?

Not if you're like me and exploit the GTS cloning glitch on Pokemon Diamond/Pearl.  Just attach a master ball to a pokemon, upload it to the GTS and switch your DS off at the split second when the pokemon is both on the GTS and on your in game PC.

I'm still annoyed I can't transfer them to Black.  At least I can still upload all my event pokemon.

That's what Master Balls are for.

i would probably start off with a Quick ball.

If failed, start paralyze/sleep followed by a DoT move (if available) and keep throwing ultra balls at it while it kills itself with recoil damage.

But you only get 1. You aren't going to save it in case a bigger catch next time?