Trump directed the presidential plane - called Air Force One when the sitting President is aboard - to pick up Bush's casket and transport it to Washington.
Bush will lie in state until Wednesday morning when his casket will then be transported to the National Cathedral for the first of two funeral services for the former president.
The 41st president died Friday at his home in Houston at 94.
President Donald Trump and his wife later paid their respects, saluting Bush. His death also reduces membership in the ex-presidents' club to four: Jimmy Carter, Bill Clinton, George W. Bush and Barack Obama.
It appears that Sully and Bush's connection was near instantaneous, with both the former president and the pup's social media accounts sharing pics of their time together. Bush will be buried next to wife Barbara, who died in April, and daughter Robin, who died of leukemia aged three.
On Thursday, Bush's remains will be flown back to Houston for a funeral at the St. Martin's Episcopal Church in Houston.
Soldiers, people in wheelchairs and long lines of other Americans filed through the hushed Capitol Rotunda on Tuesday to view George H.W. Bush's casket and remember a president whose legacy included military victory half a world away and a landmark law affirming the rights of the disabled.
She continued: "I hope readers and ticket holders will understand my decision regarding my desire to attend President Bush's funeral, and join me in paying tribute to him and his tremendous contributions to our world". Pence recalled that he recently asked Bush to sign a photo for his son, who made his first tailhook landing as a Marine aviator on the USS George H.W. Bush.
All day, thousands of people walked by his flag-covered casket.
He became a multi-millionaire in the oil industry, and was a decorated World War II fighter pilot and a former head of the Central Intelligence Agency before entering the White House in 1988.
"We're putting America first". As a younger man, he survived the destruction of his Navy bomber by Japanese gunnery, served diplomatically from China to the United Nations to the Central Intelligence Agency, then lived to see one of his sons become a war-on-terror president and another's ambitions crushed by a single hyphenated word-"low-energy"-in the Trumpian cataclysm of 2016". The pair worked together to raise tens of millions of dollars for victims of the 2004 Indian Ocean tsunami and Hurricane Katrina, which swamped New Orleans and the Gulf Coast in 2005.
Since it was built, the 4141 George Bush locomotive has delivered shipments across all 23 states served by Union Pacific, the company said.