Why do you doubt he had a high IQ? Depends what we mean by "high", but I would think any president (certainly in modern history) must have a pretty high IQ to manage so many people and issues at once. I would wager someone capable of doing that is capable is getting into Yale on merit, especially when they're younger and in their mental prime. Nothing to do with politics anyone might personally agree or disagree with: Reagan, Bush, Clinton, Obama, Trump, Biden.

For liberals (not saying you) who think Bush is dumb: is it because his policies disagree with you? Maybe people who come to different conclusions to you aren't dumber, but just have different values. Do we really think all of our political beliefs are based on intellect only? That's very arrogant imo.