It is an annoying problem... I have since bought a VERY expensive AFM to try and rectify the problem, and it is still there. Funny thing since I posted last is that the car is now off the road and is only driven 2 or 3 times a month. Since doing this she has started every time as soon as I turn the key. If I leave her for about 30 minutes after driving and then go down to try and start her, I get the same thing where I have to pump the accelerator to get her to start!!!
I have pretty much given up on this problem with my car. 4 seperate BMW dealers have looked into their records and said that this problem has come up many, many times before...way back when the cars were only 5 and 6 years old. There was a fudge introduced back then that involved splicing into and connecting the feed and return fuel line together with a one way T-Shaped valve...this reportedly solved the problem, but no one at BMW knows how to do it anymore.
I personally think that this is an injector problem. I think that all of the injectors are leaking into the cylinders while the car is standing due to the fact that the car only has a pressure regulator on the end of the fuel rail...which over time, as the injetors wear, causes the fuel rail to leak as it cannot withstand the pressure anymore. The reason that it seems better when cold is that the fuel is leaking past the cylinder heads and into the oil, which means that the cylinders are not flooded, and that is why it is easier to start. When hot, the fuel continues to vaporise inside the combustion chamber and I think that this causes the car not to start because it fouls the spark plugs.
Maybe try getting the injectors professionally cleaned or if you have money, buy new ones?
Whatever the problem is, many people on my side who have seen the car, recon it is fuel pressure related...
Another theory that I heard was that the non-return valve in the feed fuel line was stuck open and that the fuel was bleeding back into the fuel tank while the car was standing. The valve is built into the fuel pump, so you will have to replace the fuel pump.
Hope that helps
BB