[The Wind Breezes]

Long story short, it's not going to disappear even if you follow that TSB which may not apply to you anyway. You will have to live with it and plan your driving around it. I drive in full manual mode always, and the more gas I apply from a stop the less lag there is. Certain situations will induce more lag than others. It's not as good as controlling the clutch myself, but once the car is underway the DCT magic is a lot better than manual.

To directly address your question, other than using BMW standard tools or taking the car to the dealer I dunno how to find out what software version you have. Well, MHD tells you when it generates a "backup", but that's not available for your ECU. But you need to keep your expectations in check, because regardless of what other placebo-takers have written, you will never totally get rid of lag on this transmission when taking off. It's not like a Porsche dual clutch (those are totally awesome, downshift way faster and more consistently especially under duress when hot and don't have this problem when taking off).