The journey through five small Texas towns was expected to take about two and a half hours.
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.
Bush died on Friday at age 94. Mr Bush will be buried in Texas on Thursday. He will lie in state until Wednesday, when funerary services will take place at the Washington National Cathedral. The first was Abraham Lincoln following his assassination in 1865.
President Donald Trump and George P. Bush's father, Jeb, engaged in a vitriolic primary rivalry during the 2016 campaign, and Trump has mocked and criticized the legacies of both Presidents Bush. Blair House is also known as the President's Guest House.
The New York Stock and NASDAQ will be closed for the day.
Escorted by former Secretary of Homeland Security Tom Ridge, Sully watched as mourners paid their respects to the late president, whose casket was covered with an American flag, alongside a red, white and blue flower wreath. "We spent a week there working with President Bush's team", Hibbard said. It was one of the few times the company has painted a locomotive any colour other than its traditional yellow. He also called the locomotive "the Air Force One of railroads". He died on November 30 at the age of 94.
Walesa said ahead of Wednesday's ceremony for Bush, "Therefore, when I say goodbye, I want to say that the fight goes on, that we disregarded democracy in Poland, we let the populists and demagogues win".
Bob Dole, 95, an advocate of that legislation and the former Senate majority leader from Kansas, came in a wheelchair to honour his fellow Second World War veteran. Alan Simpson and presidential historian and Bush biographer Jon Meacham, none of whom are expected to critique Trump in their statements.
Bush was elected president in 1988 after serving 2 terms as President Ronald Reagan's vice president.
There were chills for sure in Smithtown, where Sully was trained by America's VetDogs.