I will preface this by saying I do not have a lock on BMW's, especially older ones, so take this for what it's worth.
If this were an American car with mid 90's fuel injection, I'd say your Mass Air Flow (MAF) sensor was bad. Since it's a BMW and it appears they didn't use a MAF, I'd point to the air flow meter. Here is my thinking. I'm going to make an assumption that BMW's go through two phases of running, that being open loop and closed loop. Open loop mode is where the engine is at start-up and is not warmed up yet. The Engine Control Unit (ECU) does not utilize some of the sensors at this point (ie: O2 sensors and air flow meter), but rather relies on the throttle position sensor and some others. When the engine is warmed up enough, it switches over to closed loop mode, in which it uses all of those sensors.
While this may not be exactly the scenario, it seems likely that one or more of the control sensors which helps the ECU decide how much fuel to dump may be bad (or not responding correctly), so the amount of fuel which is dumped into the engine is out of whack and therefor makes the engine run completely different once it switches modes. Since the air flow meter is a very expensive part and you can only get them as rebuilt (not new ... at least not from the parts stores), I will NOT suggest you run down and just replace this. Take it to a skilled mechanic who can diagnose this for sure, as Alan has stated. I could be completely off base not knowing exactly how BMW control systems work.