IOTL, George W. Bush and Jeb Bush ran for governor of Texas and Florida, respectively. George W. Bush won, while Jeb Bush lost by under 64,000 votes to Lawton Chiles, whose lieutenant governor, Buddy MacKay, would lose to Jeb Bush in 1998.
But, WI Jeb Bush ran a better campaign and won against Chiles in 1994? What are the ramifications for the 2000 GOP nomination?
According to Wikipedia, George W. Bush launched his candidacy after being encourged by George Shultz to run. Shultz also introduced him to policy experts to talk about serious matters and see if he had
presidential material. But if ITTL there's another popular Bush who just got re-elected as governor of Florida in 1998 (a state that Bill Clinton won in 1996), it's very likely that Shultz would have approached him instead of his brother (who actually had less political experience).
Let's assume that ITTL Jeb Bush
somehow manages to defeat Sen. John McCain (I'm not so sure that he could've) and takes the Republican presidential nomination. What's next? It's very likely that he would've chosen Fmr. Sen. John Danforth (R-MO) as his running mate instead of Dick Cheney (IOTL, Cheney actually expected GWB to choose Danforth), and it's even more likely that Vice Pres. Gore would've beaten him in the presidential election. Why? Because he did an awful campaign in 2016, and I don't see why he would've done better in 2000.
That said, it's worth exploring the possibility that ITTL McCain could've defeated Jeb Bush in the Republican primary and
possibly beaten Gore. However, that would've been a weird victory by OTL's standards because McCain could've won states like Connecticut, Michigan, New Hampshire, Oregon, Pennsylvania, Vermont, Washington and Wisconsin (where he did very well in the primaries), while losing others like Arkansas, Kentucky, Louisiana, Missouri, Tennessee and West Virginia. I'm not sure how well he'd have done with Latino voters (considering the fact that Bush did extremely well with Cuban and Mexican voters), but if ITTL he does worse than Bush with them, he could've lost Colorado, Nevada and Florida to Gore (the latter is specially in danger if we butterfly away the Elián González affair, in which case the Republicans would've been doomed in Florida). In any case, Gore has the upper hand because McCain was weak in the South and Sens. Lieberman or Kerry (depending on who he'd chosen as his running mate) would've helped him to protect some of the Northern states (and in the case of Lieberman, also Florida), blocking McCain's path to victory through those states. If you think about it, Dubya was actually the "best" candidate that the GOP could've put up in the 2000 election (regarding winning the election, not governing).