According to GOOGLE Earth it sits at just over 8,900 feet (8916). This makes sense based on it's location above Golden Gate Canyon. On a side note, Bear Paw Road is one of the few in the area that is a relatively easy grade and without too many switchbacks. Likewise the driveway isn't nearly as bad as the across the street neighbor who needs to wind up 6 hairpin turns just to get into the garage!
Here's the GOOGLE link: