I wish I had spotted this thread when you first posted, before you did any work. I have some experience with this type of repair.
First off: BMW uses different colors of primer-filler under the base color coat, to minimize the visibility of the inevitable stone chips. On a white car, your filler coat would be a dull white. The fact that your damage was black means the primer-filler was scraped away as well, which means you painted an
unprimed surface.
The Dr. Colorchip paint may or may not be suitable for use on bare metal or plastic on repairs larger than a stone chip--that is, you may find this repair falls apart in several months because the paint did not adhere properly to the unprimed bodywork. However, it is a different formulation than typical touch-up paint and it may be self-priming.
Bottom line, check the repaired area often for signs of cracking, chipping or peeling. If it starts to let go, before you engage a body shop you might still want to try a "proper" repair yourself.
This thread outlines the process I followed to effect repair to a similar scrape. Over a year has passed since and the repair is still undetectable. The work may seem daunting at first but it helps to remember, the worst that can happen is you pay a body shop to repaint the bumper cover--which is exactly the same outcome as never trying to repair it yourself in the first place. :thumbup:
In any event, I hope your Dr. Colorchip repair holds and if it does not, I hope my brief photo essay proves helpful.