Eulogies will be offered by George W Bush, former Wyoming senator Alan Simpson, former Canadian prime minister Brian Mulroney and historian Jon Meacham, a Bush family spokespeople said.
Bush was president from 1989 to 1993, a time in which communism toppled across Eastern Europe and Walesa became president of a democratic Poland.
It will be the eighth funeral train in US history and the first since Dwight D. Eisenhower's body travelled from the National Cathedral in Washington through seven states to his Kansas hometown of Abilene 49 years ago. Dole would go on to be the Republican presidential candidate in 1996, but would lose to former President Bill Clinton.
President Donald Trump tweeted earlier Tuesday that Mrs. "It's a good thing that the dog is moving on to another gig where he can be helpful to other people (rather than becoming another Bush family pet)".
Bush, father of the 43rd president, George W. Bush, will be buried on Thursday in Texas.
Trump and his wife joined mourners at the Capitol Rotunda Monday night.
Vice-President Mike Pence and Republican Senate leader Mitch McConnell also spoke. The Bushes are staying there.
Bush was elected president in 1988 after serving 2 terms as President Ronald Reagan's vice president.
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Across France, four people have been killed in accidents linked to the demonstrations and road blockades, and hundreds injured. A joint statement from the CGT and FO trucking unions protesting a cut to overtime rates called for action from Sunday night.
Bush, the 41st USA president, occupied the White House from 1989 to 1993, navigating the collapse of the Soviet Union and expelling former Iraqi President Saddam Hussein's forces from oil-rich Kuwait.
Mr Bush's passing puts him in the Washington spotlight after more than two decades living the relatively low-key life of a former president.
"His character speaks most, because of his character, how he handled so many important points in our history".
The New York Stock and NASDAQ will be closed for the day.
Come for a beloved presidential pet, and the internet comes for you.
He arrived in the Capitol rotunda in a wheelchair pushed by an aide. The first was Abraham Lincoln following his assassination in 1865.
Bush was born into privilege and politics (his father a US senator and grandfather a top industrialist).
Bush greeted former and current presidents and their wives on the bench with handshakes before having this heartwarming exchange with Michelle, who couldn't help but chuckle as she was handed the mint.