I don't think Bush actively planned things out this way. There's the video comparing how he talked in the gubernatorial debates against Ann Richards to his performance against Kerry -- back in the old days, he seemed to be trying his best to look smart, speaking clearly and rattling off facts and policy proposals.
In 2000, the media played up the Bush versus Gore contrast as a simple Texas yokel versus an cold-blooded intellectual. It so happened that Bush won, though I really don't see reason to think the contrast in level of education actually worked in his favor. But what happens in the wake of victory is that the media spins every feature of the winner, especially the ones it's made most salient, as winning traits. The converse happens to the loser.
Many in the next generation of Republican politicians -- Cain and Palin, for example -- took their lessons from the story the media told them. While Bush more or less backed into the position of the proudly uneducated person by accident, they came to regard it as a winning political strategy. Moreover, it's a strategy that fit them really well. Absorbing complex policy views, even if they're crazy, takes some work and intellectual effort. Cain and Palin weren't up for doing that, whether for reasons of ability or time or sheer laziness. So they pursued the supposed winning strategy that was open to them.
The funny thing is, I don't actually think Republican primary voters actually put a premium on this. They have high opinions of people like Paul Ryan and Newt Gingrich, who have all kinds of complex views about policy and don't actively try to come off as ignorant.