They were fellow World War II veterans, Republican Party leaders, fierce rivals for the 1988 Republican presidential nomination won by Bush ("Stop lying about my record", Dole snapped at Bush) and skilled negotiators.
One of Bush's major achievements was assembling the worldwide military coalition that liberated the tiny, oil-rich nation of Kuwait from invading neighbor Iraq in 1991.
President Bush tweeted then that it was, "A great joy to welcome home the newest member of our family, 'Sully, ' a attractive - and beautifully trained - lab from @AmericasVetDogs".
The two-year-old Sully has been at Bush's side since June, just weeks after the death of the president's wife Barbara, to whom he was married for 73 years.
Bush's grandson George P. Bush will give the other eulogy.
President Donald Trump had no speaking role during the Episcopalian service, a break from recent tradition and in accordance with George H.W. Bush's wishes.
The Kansas Republican, with some help from an aide, stood from his wheelchair to salute the late Bush as he lay in state at the Capitol Rotunda. December 5 to honor the 41st President of the United States, George Herbert Walker Bush.
George H.W. Bush is going to his final rest in Texas.
Mourners laughed as Baker recalled how Bush would let him know a conversation was over: "Baker, if you're so smart, why am I president and you're not?"
Instead of honest, balanced tributes which delivered a full picture of Bush's life and legacy, the media seemed to favor hagiography, retelling the former president's life with its blemishes removed. He praised Bush as a "truly attractive human being" who had the "courage of a warrior but the greater courage of a peacemaker". By evening, his casket was at St. Martin's Episcopal Church in Houston.
Mr Trump has ordered the federal government closed for a national day of mourning while flags on public buildings are flying at half-mast for 30 days.
Both U.S. Post Offices will be closed in Kingman, as well as the U.S. Bureau of Land Management field office in Kingman.
Democrat Bill Clinton coasted to victory, ending Bush's presidency.
Trump has often aimed political taunts at the Bush family, long a symbol of the traditional, more moderate wing of the U.S. Republican party that often is at odds with Trump's populist supporters.