Google has been working on this AI problem since probably 2008 or so and been road-testing self-driving cars since 2011. As far as I know BMW has no development at all on this concept.
BMW has been making cars since 1916. How long has Google been making them? How hard is it for established manufacturers to get the tens of thousands of parts in a road car 100% correct at design time? Google is not infallible. If they do indeed decide to mass manufacture their own cars (which I doubt) it will take years and billions of miles to iron out all the issues. Engineering isn't software.
Say you're BMW's favourite kind of customer: you buy new, all the gimmicks, change your car for another BMW every 4-5 years and have been doing so for 20 years. Are you going to start buying Google's plastic toy car that's only been in production for 2 years instead? You might buy one to go with your BMW, especially if you live in a city, but you're still going to buy the BMW.
Research and development is an extremely long process, there, and as far as I know BMW's R and D is focused on building cars.... they probably don't have people who even know about robotics, let-alone AI for the self-driving problem.
Presumably they'll do what Google, Apple, FB and the rest of the tech-cartels do when they want to muscle in on something: buy it in.
Actually, having said that, I very much doubt BMW will be competing with Google for car sales anyway, because I very much doubt Google will be retailing their cars. They will either operate the fleet themselves or sell them to other fleet operators or just sell the software.