Other potential candidates were as followed, I have given a info on them and their age in 2000.
Gov.
John Engler of Michigan (52) - Roman Catholic, so may have friction between United Methodist, Bush. IOTL 46th Governor of Michigan from 1991 to 2003.
Sen.
Bill Frist of Tennessee (48) - Helped Bush Sr. campaign in Tennesse. IOTL Senate Majority Leader from 2003-2007
Sen.
Chuck Hagel of Nebraska (54) - A recipient of two Purple Hearts while an infantry squad leader in the Vietnam War, Hagel returned home to start careers in business and politics. IOTL he was the 24th United States Secretary of Defense under President Obama
Gov.
Frank Keating of Oklahoma (56) - As governor, he oversaw the state's response to the Oklahoma City bombing, which could help if he can advice Bush to be more responsive during 9/11. IOTL He served as the 25th governor of Oklahoma from 1995 to 2003.
Sen.
Jon Kyl of Arizona (58) - He received his bachelor's degree and law degree from the University of Arizona. IOTL he was Senator from 1995-2013 and Senate Minority Whip from 2007-2013. In 2010, he was recognized by Time magazine as one of the 100 most influential people in the world for his persuasive role in the Senate.
Sen.
Connie Mack of Florida (60) - He was considered as the Vice-Presidential nominee on the GOP ticket by Bob Dole in 1996. IOTL he left the senate in 2001.
Gov.
George Pataki of New York (55) - Having a new york politican in power may help during 9/11. IOTL he was the 53rd Governor of New York 1995-2006.
Gen.
Colin Powell of New York (63) - He has served as National Security Advisor (1987–1989), as Commander of the U.S. Army Forces Command (1989) and as Chairman of the Joint Chiefs of Staff (1989–1993), holding the latter position during the Persian Gulf War. IOTL would be Secretary of State under Bush.
Gov.
Tom Ridge of Pennsylvania (55) - Another Roman Catholic and served in Vietnam. IOTL He was the 43rd Governor of Pennsylvania (1995–2001), Assistant to the President for Homeland Security (2001–2003), and the first United States Secretary of Homeland Security (2003–2005).
Sen.
Fred Thompson of Tennessee (58) - American politician, actor, attorney, lobbyist, columnist, and radio host. IOTL He served as Senator from 1994 - 2003
So really there is a fair choice.
Here is a really good picture to use if you want Former Senator for Missouri, John Danforth, to be sworn in as Vice President.