I know you can buy it anytime before 50K. You can also buy it after 50K, but there is a surcharge. Also, there are different levels of coverage. I think they call them silver, gold and platinum. Platinum is what you get under your usual new car warranty. I think gold excludes a couple of items like navigation. And, I think silver is just the power train.
If it was me, I would go for the platinum. I have about 45K on my 2011 X3 now and was considering the extended warranty. But, I'm going to pass and take my chances. The engine, mine is the inline 6, is bulletproof in my opinion. The tranny so far is perfect. I've had the inline 6 in my previous two BMW's and haven't had to touch either one. My first inline 6 had about 250K and ran like new. My second one was an M3, but I only kept it long enough to put 125K on it.
My concern with BMW's is usually focussed on the electronics and the front suspension. Everything else is extremely good, especially for the first 100K.