Asteroid apparent magnitude I'm writing an SF story in which a main belt asteroid is diverted into a collision course trajectory with earth (long story), and unknown to us here on earth. 

Its H magnitude is 12. As it nears earth, I would assume it gets brighter in V--apparent magnitude. Considering all the eyes on the sky these days, how bright, apparent mag V, would it get before being discovered here on earth? 9 or 10 seem reasonable?

And if you could give its distance in AU, at discovery, that would be super (trying to find out how much time we have left ;) )!
That's a big asteroid!

Recent discoveries of objects of this size are rare, one example was 2013UQ4. We believe that all objects of this size in the main asteroid belt have been discovered. (The discovery of 2013US10, which appeared to be main belt object turned out to be an error, the combination of observations of two different objects) This object has a highly inclined and retrograde orbit. It turned out to be a comet not an asteroid. 

For context US10 it was at magnitude 19 when discovered. It is unlikely that a large body would remain undiscovered until it was at mag. 10 or 9, especially if it was in the main belt. A very small object that is rapidly brightening could reach these magnitudes before discovery, but not a 10-20km sized object that your story implies.