Now that you've raised it though, I think it's worth considering that GWB at least understood the office he was taking (setting aside how I or others feel about the actual decisions taken). I don't feel like your next president understands this at all, and certainly I don't think even his supporters see any reverence for the office.
I see no evidence, even now, that he has any grasp of the situation he is in, which is incredibly dangerous for global stability.
The point I'm trying to make is that I think there's a very good chance that history will remember GWB more favourably after the next 4/8 years are behind us.
I thought both that Bush was one of the very worst presidents in US history AND that he compared favorably (above average) to other world leaders in his time.
Before Trump, we could take it for granted the US president was a serious person who cared about having the country do well and wasn't interested in anything resembling an authoritarian takeover. (Even Richard Nixon had plenty of lines he wouldn't cross, some of which Trump already has.)
Trump is incomparably worse than Bush as a choice for President.
I also had a small amount of more direct exposure in the late 70s, and it fit the pattern.
Now, these "smarts" were more in the way of getting to a quick, non-stupid analysis of a situation than they were about really deep thinking or about having a nose for additional facts to seek out ... but that pattern fits Bush.
Bush's gift was the ability to be charming. But it's pretty clear he isn't even close to being the smartest person in almost any room, let along a room full of Stanford students as the made-up OP story described.
HBS students in those days were, as a group, pretty smart.
Bush's real intellectual shame as president was his ignorance. He didn't think hard about most public policy issues until he decided to run in 1999. His debate statements were pretty obvious bluffs. I referred to him as "evil" for running despite being so ignorant and hence unqualified.
None of that precludes him having figured most of it out by the time he'd been president 4-6 years.
I really, really, really, really wish our current President-Elect had 1/3 the understanding Bush took office with. :(