Look at his grades at yale. That is enough evidence of his intelligence. How many forum members here do YOU think could get into Yale?
Well, maybe if my father, grandfather, and great-grandfather had gone there, I would have gotten in too with C's in high school. I don't see how you think that just because Bush attended Phillips Exeter and Yale (both of which are thanks to a wealthy family and legacy connections) that he's naturally smart.
In real life, I got rejected from Yale and I had over a 4.0 high school GPA. Good thing Columbia didn't feel the same way.