<<medium old bmw>>
If it's among the older BMW's that had mechanical injection (aka BOSCH K-Jetronic) then this may just be a quirk. My sister's 1982 320i has K-Jet and it seems to pick and choose how long it takes before it starts. It always starts and it runs very well, though it does not like to idle when it's cold (in the winter you have to start it just like a carbbed car). My Accord used to pick and choose when it wanted to start, sometimes taking up to 10 minutes of on-off cranking. After changing the plugs, wires and the distributor cap/rotor (which did turn out to be cracked), I finally changed the fuel pump relay and this cured things. Probably just a quirk in your case though, since it's not taking excessive time to start. Good luck with it though.
Zenmervolt