A similar outpouring is anticipated in Washington this week during the state funeral for Bush, who died late Friday at his home in Houston.
Bush will lie in state at the Capitol through Wednesday, as members of the public are allowed to file through the Rotunda for a viewing.
George H.W. Bush's death comes less than eight months after losing his beloved wife of 73 years, Barbara.
George H.W. Bush's body continued to lie in state Tuesday at the US Capitol, where officials said more than 26,000 people so far had come to pay their respects.
Bush was being transported aboard the presidential Boeing 747 - made available at Trump´s direction - from Houston to Joint Base Andrews, in Maryland. "For in all his 94 years, President Bush never lost his love of adventure and he never failed to answer the call to serve his country".
Scott Moore, Union Pacific's Senior Vice President of Corporate Relations, says he expects people will use Bush' funeral train route to pay tribute and reflect on the life of the former president. There is a stark contrast with the funeral of Senator John McCain in September, to which the president was not invited and where anti-Trump sentiment was palpable.
He served as ambassador to China, director of the Central Intelligence Agency, and vice president to Ronald Reagan before winning the White House.
George W Bush and others from the family travelled on the flight from Houston.
"We'll be spending three days of mourning and three days of celebrating a really great man's life", Trump said.
Thursday, 6 December, 11 am: Funeral service at St. Martin's Episcopal Church.
A humble hero of World War II, Bush was just 20 when he survived being shot down during a bombing run over a Japanese island.
At one point, George H.W. Bush and Bill Clinton did not get along. Flags on public buildings are flying at half-staff for 30 days out of respect for Bush.
However it is unclear if 94-year-old Jimmy Carter, who was president from 1977 to 1981, is well enough to attend.
Both Bush's wife Barbara, the former first lady who died in April, and their daughter Robin, who died of leukemia as a child, are laid to rest on the library's grounds. He had joined the Navy when he turned 18. The couple was married for 73 years, longer than any other US presidential couple.
But despite Bush's record approval ratings after "Desert Storm", he disappointed Americans on the domestic front.
Bush's death has also led to a series of symbolic moments.
After the war he started an oil business in Texas before entering politics aged 40. He was elected to the first of two terms in Congress in 1967. After leaving the White House, Bush forged a close friendship with Clinton, and together the two raised millions of dollars for victims of Hurricane Katrina and a devastating tsunami in southeast Asia. "But if we respect the human being, I think it's a much broader framework for civility and good will in the country".