Had similiar problem recently on my 2001 E53. Replaced the faulty bulb with a new one, but still wouldn't work. Turns out the socket was corroded and needed major cleaning and scraping with a sandpaper. Not an easy job considering the confined space - but worth saving dealer replacement. All is fine now.
Interestingly, I found that if you have the key in the ignition and electrics turnd on (to see if your bulb is working) and you replace a bulb, it doesn't work. Drove me crazy. Only if you switch off the electrics and then back on again it will work.