If it comes on and goes off, that suggests more of a ballast issue, not a bulb issue. A dead bulb usually turns pinkish or a different hue is it is going bad...and eventually won't fire at all. If it turns on and then goes out, it sounds like a different issue, most likely the ballast.
What you can do is swap bulbs between your passenger and driver side and see if you get the same problem. If you do, then you will need to change out the ballast. A new ballast will cost a couple hundred dollars.
Like I said before, you would probably need 2 bulbs, unless you don't mind one headlight being a different color or brightness/intensity than the other. Here's a link to Amazon. Philips and Osram are the most respected HID bulb companies in the automative lighting industry.
The easiest way to change the headlight bulb is to go through the wheel well...you have to take off the wheel well cover (very easy or pry to the side) and then reach in and change the bulb. I'll send you a link how to do so. If you don't want to remove the wheel, you can turn the wheel all the way to the right or left to reach the bulb.
Here it is: