The fight for the 2000 Republican nomination was a bit odd. George W. Bush was basically running against a bunch of also-rans that no one took seriously until McCain came out of nowhere to be his most formidable foe. A lot of the old Reaganites who were suspicious of the establishment rallying around Bush gravitated to McCain once his campaign took off. Then McCain decided to run as an odd mix of Rockefeller Republican and deficit hawk and the Reaganites came back to Bush. I'm convinced McCain's campaign hurt Bush a lot by sort of poking holes in the illusion that Bush was the next step forward for conservatism. In 1999 or thereabouts, most of the Republican base was steadfastly behind Bush and saw him as the Republican response to Clinton, for lack of a better description.
Without Bush, the establishment would have wanted another candidate to get behind, and I doubt they would have waited for McCain to make his maverick run. I'm assuming in this ATL, Bush doesn't run because he loses to Ann Richards in 1994 or something. I assume we are also going with Jeb having lost in 1994 as well. That probably rules out both Bush brothers. In that case, the establishment would have looked to other center-right governors who could combat Clinton's "theft" of soccer moms (who used to vote Republican before 1992). It becomes difficult to think of someone off the top of my head who was photogenic and telegenic enough to fit the bill of establishment candidate. Wisconsin Gov. Tommy Thompson and Michigan Gov. John Engler wouldn't have been ready for prime time due to their stout appearance. Perhaps Oklahoma Governor Frank Keating would have been drafted?
If no establishment candidate scooped up all the oxygen in the room (e.g., let's say that Keating, along with Tom Ridge and John Kasich, all make a run for it without anyone really exciting the base), then McCain might have very well won the nomination when his bid took off after New Hampshire's 2000 primary. That leads to the ATL McCain v. Gore race and lots of butterflies.
Also, I doubt GWB tries for the presidency at a later time if he doesn't run in 2000. That was Bush's year. People were tired of Clinton and a lot of voters who were sold on the notion that Bush 41 was bad by Perot in 1992 were regretting their decision and remembering the Bushes fondly. By 2004, even if Gore were POTUS, the country would have moved past the Bushes.
