It's fairly unlikely the bulb burnt out - I'd say the ballast kicked the bucket. They work a lot like fluorescent bulbs, actually - and in those, 80% of the time when they don't work it's either the starter or the ballast (both of which are contained in the ballast unit on an HID setup).
2012 GT Premium Coupe 6MT
Kona Blue | Black/Grabber Blue
401A | 3.55 | BBP | CP | SP | EP | GR | HID | RVC | RSS | "Piss 5ohwhoa off"