Ok, I've just done this job for the first time. Front right light rings were out. computer error message alerted me to it. This is a pain in the A! First you need to buy new bulbs. Buy online and get the LED aftermarket ones. They're cheaper and brighter and use less wattage. I'm in Melbourne AUS and bought them on ebay USA. they were $55USD for two. BMW Australia wanted $73AUD for 1! this is such a pain in the ass job that you should do both lamps while you have the front bumper off. There is one bulb for each headlamp. Each bulb drives the two rings in each headlamps.
Yes, the bumper needs to come off. Remove, the left and right lower plastic grills. (black lower plastic grills) These lever out. No screws. You'll see some bolts holding the bumper in place. Remove the front number plate and chrome grill moldings. Centre one first, then left and right. Disconnect the 4 front parking sensor plugs. You'll see more screws holding the bumper on. There are another two screws on each side near the wheel arches.Unscrew the bolts holding the headlamp washer cover. Unscrew the headlamp washer units. (no need to disconnect). Undo all bumper screws.
Now this is important, the bumper is held on each side by two plastic lips. The bumper needs to he lifted slightly up and forward over these plastic lips.
Bumper should be off. There are 4 bolts holding each headlamp in place. You'll need to get an extension wrench to reach the two near the air intake box. The headlamps lift out forward. You'll need to disconnect the indicator plug for the headlamp. No need to disconnect the big one for the xenon's. The bulbs for the angel eyes are inserted upside down from beneath the head lamp. There's a cover. Remove this then turn the lamp anti clockwise to release. Replace an install in reverse order. I hope this helps as I struggled to find much on the internet on this.