He died on November 30 at the age of 94.
Vice President Mike Pence and Republican Senate leader Mitch McConnell also spoke.
The train is a Union Pacific Corp locomotive, numbered 4141 and bearing the name "George Bush 41" on the side that has been in service since 2005.
Before the public started walking past Bush's casket, USA political dignitaries praised him as an American hero in World War II, a statesman, a world leader and, perhaps most of all, as a decent man full of grace.
Fformer President George H.W. Bush and his wife Barbara wave out the window of a new locomotive numbered 4141.
Wednesday, 5:45 p.m: A service is held at St. Martin's Episcopal Church in Houston before Bush lies in state until Thursday at 6 a.m. Trump sent the presidential plane to Houston to bring his body to Washington, D.C. The president and first lady will attend his memorial service at Washington National Cathedral on Wednesday, but the president will not deliver a eulogy.
Also, in the front row was Democrat Bill Clinton, who defeated the elder incumbent Bush in 1992 to become president, and his wife, former Secretary of State Hillary Clinton, whom Trump defeated in the 2016 election.
Cannon fire roared again outside the Capitol as the sun sank and the younger President Bush stood with his hand over his heart, watching the casket's procession up the steps.
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In a drizzling rain, former U.S. President George H.W. Bush was buried Thursday at his family plot behind the George H.W. Bush Presidential Library and Museum at Texas A&M University.
The locomotive was painted to resemble Air Force One, but George H.W. Bush joked that if it had been around during his presidency, he may have preferred to ride the rails rather than take to the skies.
During the two-and-half-hour ride, the train was welcomed by thousands of people along the rail tracks, paying respects to the late president and experiencing history.
Bush was hailed by presidential historian Jon Meacham as "America's last great soldier-statesman", who "made our lives and the lives of nations freer, better, nobler and warmer".
Bush died last week in Houston at age 94.
"I think he was one of the kindest, most generous men", visitor Marge Frazier said.
Bush's son Jeb Bush expressed his appreciation for Dole's tribute on Twitter, writing, "Just incredible". Both served in World War II.
Flags on public buildings are flying at half-staff for 30 days.