could also be the non return valve in the fuel pump has had it, if the engine turns over ok the starter is fine, it'll start from cold because the cold start injector will give it the extra burst of fuel it needs to fire which in turn opens the metering flap and pulls fuel through to the main injectors, same applies to bump starting.
if the non return valve has had it there will be no risidual pressure to the metring head which is why when you crank if you are liucky itll fire but only briefly, after that you need to just crank the engine which will eventually get rid of the air lock created in the injector pipes and start,

this may sound crazy but i had the same thing on my s1 and my rs1600i, both were ok from cold and would only warm start if tried within 5 minutes or bumped or if i pushed the flap down on the metering head,
you can fit an aftermarket non return valve after the fuel pump but just make sure its rated at min 7 bar pressure