Dubya wins his 1978 congressional race, and the butterflies from that are enough to make the Reagan/Ford ticket happen. Not chosen as Vice President, H.W. instead finds a place in Reagan's cabinet, albeit missing out on Secretary of State. Dubya runs for the Senate in 1984, and come 1988 both Bush's are seen as potential presidential candidates, but the family instead opts to field Dubya, sensing his popularity within the party and a tiny bit worried about Bush Sr.’s lack of recent political experience. Bush wins against Gary Hart in a close election, but is assassinated in 1991.
H.W. finds himself back in cabinet shortly thereafter, finally being appointed Secretary of State by longtime friend Alan Simpson, though his time in office is brief as Simpson is defeated by Paul Tsongas in 1992. By 1996, though, the Democrats are in a tough spot following Tsongas' resignation and Bush's presidential aspirations haven't gone away, and he manages to win the nomination and the general election in part by seizing upon Dubya's legacy.
Presidents of the United States:
1981-1989: Ronald Reagan / Gerald Ford (Republican)
-80: Jimmy Carter/Walter Mondale (Democratic), John B. Anderson/Patrick Lucey (Independent)
-84: Walter Mondale/Martha Layne Collins (Democratic)
1989-1991: George W. Bush / Alan Simpson (Republican)
-88: Gary Hart/Fritz Hollings (Democratic)
1991-1991: Alan Simpson / vacant (Republican)
1991-1993: Alan Simpson / Richard Lugar (Republican)
1993-1995: Paul Tsongas / Bruce Babbitt (Democratic)
-92: Alan Simpson/Richard Lugar (Republican)
1995-1995: Bruce Babbitt / vacant (Democratic)
1995-1997: Bruce Babbitt / John Breaux (Democratic)
1997-2005: George H. W. Bush / John McCain (Republican)
-96: Bruce Babbitt/John Breaux (Democratic), Richard Lamm/Tim Penny (Alliance '96)
-00: Bob Kerrey/Dottie Lamm (Democratic)
2005-present: Carole Keeton Strayhorn / Bill Bradley (Democratic)
-04: John McCain/Jim Ross Lightfoot (Republican)