Here's one way: have Bush win the 1978 congressional race that he lost IOTL to Kent Hance. After spending the 1980s and early 1990s in the House, he then runs in the Senate special election in 1993 and wins (I doubt he'd beat Bentsen in 1988 or Phil Gramm in the 1984 Republican primary). He then runs (and wins) the Republican nomination in 2000.
Meanwhile, with no W. in 1994, Richards wins reelection in that year (one of the few Democratic governors to do so) and challenges and beats Gore in 2000.
Volia: it's Bush vs. Richards in 2000...