I had Adaptive Drive on my 2012 X6 50i. Loved it.
For the 6-series, it is an add-on option and not part of M sport (was in 2014 for sure) and something like $3,500.
I test drove 2013 650xi GC and LOVED It - to me it was worth every penny.
My 2014 does not have it (bought off of dealer lot and very few dealers ever added this $$$ option to a car for stock). I miss it. A lot. I think I would like my car a lot more if it had Adaptive Drive.
As for the button, I'm not sure it has one. The best way to tell is to use the BMW VIN decoder (
http://www.bmwarchive.org/vin/bmw-vin-decoder.html) - it will be shown under options.