For bleeding, try elevating the car. Air rises, so your more likely to get more air out of the system with the engine elevated a few inches.
To bleed the system run the car for several minutes until the temp is within normal range. Then turn the heater on MAX. This will cause the thermostat to open circulating more coolant through the system. Then you can open the bleed screw.
My fan clutch has failed too and my car was the same way. It started overheating until i got onto the highway or drove pretty past. In normal traffic it would overheat pretty quick. Its good to catch early because in some cases it can cause the fan to disentegrate causing massive damage and ripping through hoses. Hit up www.bimmerspecialist.com
for a replacement. I find their prices to be quite competitive. I use them for all of my OEM parts.