I have been having this same issue with my drivers side for about a year now, although it has been very intermittent. My headlight will usually fire when it is warm out (or when it is at the stealership!!!), but not always when it is cold.
I just started moving parts around, until I could follow the problem with a part move.
First, swap the bulbs. (This had no effect on mine, problem stayed on driver's side, proving bulbs are fine.)
Second, swap the ballasts. (This required removal of the headlight assemblies from the car, but it was pretty easy. This also had no effect, so ballasts are not it.)
Lastly, swap the igniters. (This is a PITA, as you need to completely disassemble the headlight assembly and put everything back together, then re-aim the headlights.) The problem followed this swap, as no my passenger headlight doesn't fire right away. I guess I will be replacing the igniter on that side, and hopefully I'll be good to go!