Hope you got my PM. In the PM I said the size was D2S but I see you found it was D2R.
Those are both good prices on the bulbs. If the dealer says thats what the problem is, then go right ahead and order the bulb and swap them out. Since you already removed it to take to the auto parts store then you should be able to replace it.
You wont be able to see the ballast its attatched somewhere on the forward frame of the car to replace HID theft. Its the "igniter" for the HID system so to speak. I'd try the bulb first just as its the easiest thing.
One word of advice, wear medical rubber gloves you dont want to touch the glass. You may also want to order two bulbs and replace them both just to ensure even lighting, although HID lamps aren't supposed to dim as they age.
The HID lamps SHOULDN'T have burned out. They're supposed to outlast the car. However, sometimes things like voltage spikes, contamination etc happen. I'd say order the bulb from the $77 place (as long as its phillips) and replace away!