If there were no limits on the number of terms a President could serve, do you think Bush would have gotten the Republican nomination again or would the incumbent lose his own party's nomination?

I think he'd have gotten the nomination again, by hook or by crook. But if we take your hypothetical change back a bit further, we'd actually have Bill Clinton running for his 5th term in office.

He'd be into his first term at best, because Clinton would have won in 2000 if there were no term limits. (If you think about it, Reagan was at his end in 1988 (the Alzheimers really hit hard just a few years later), and none of his predecessors going back to Eisenhower could have gotten a second term, all other counterfactual things being equal, making possible George H. W. Bush's election, but once Clinton was elected, he probably could have continued for another term at the least. I don't know if Bush would have been as horrible in a 2004-2008 term as he was either in his first term (he barely beat Kerry) or over 8 years (the worst president ever), but he probably would have engineered the nomination and would probably be trailing Obama by 15-20 points. McCain's saving virtue at this point is that he has had, rightly or wrongly, the reputation as sometimes challenging his party and being moderate on issues, despite his strongly right-wing voting record. Bush wouldn't have any such thing at all to boost him. He's at about 19% approval now, and those dead-enders plus Diebold shenanigans wouldn't be enough to put him over the top, even if Obama was running with Al Sharpton.

Okay let's forget about Clinton. Let me make it more specific...what if term limits were done away with during Bush's administration?

I think Bush would have gotten the Republican nomination easily. The party base - conservatives and religious zealots - love him. They're the same people who flocked to McCain once he picked Palin for VP. In a general election matchup, Obama would be winning by slightly more than he's leading McCain right now - the reasons for that having to do more with Obama than with Bush.

If another Bush term was remotely possible, the Dems might -- MIGHT -- have had the balls to impeach him and Cheney, as they should have by any minimal standard of justice.