They paused steps from Bush's casket for a minute, with Trump saluting and Melania Trump placing her hand over her heart, before they quietly walked away.
Five U.S. presidents assembled at the Washington National Cathedral for Wednesday's state funeral for George H.W. Bush, who died last Friday in Texas at the age of 94.
Vice-President Mike Pence and Republican Senate leader Mitch McConnell also spoke.
"He taught us public service was noble and necessary", his son and the 43rd president, George W. Bush, told the invited guests at Washington National Cathedral. After the World War II, he was enrolled at Yale University and got a degree in economics.
At the earlier service at Houston's St Martin's Episcopal Church, where Bush and his family regularly worshipped, the choir sang This is My Country, which was also sung at Bush's presidential inauguration in 1989.
Glasser, who described the late Senator John McCain's funeral as a "meeting of the resistance" was back again for Bush's sending off, this time to remind her followers how "extraordinary" a thing it is for a country to have two presidents from one family. There will be no mail delivery Wednesday.
President Donald Trump wasn't in attendance Thursday, but Baker seemed to draw a gentle contrast by saying Bush respected vanquished adversaries.
George HW Bush's Service Dog Sully Pays Respects To The Late President. Credit PA
Although Mr Bush's funeral services are suffused with the pomp afforded to U.S. presidents, by his choice they will not include a formal funeral procession through downtown Washington.
Bush and family pose in front of George H.W. Bush's official portrait, which is draped with black cloth.
"Looking forward to being with the wonderful Bush family at Blair House today".
"He was so qualified, and I think he was just a decent man", said Sharon Terry, touring Washington with friends from an Indianapolis garden club.
Flags on public buildings are flying at half-staff for 30 days. He will then join Walter Reed Military Medical Center working with wounded US military veterans.
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.
Union Pacific originally commissioned the Bush locomotive for the opening of an exhibit at his presidential library titled "Trains: Tracks of the Iron Horse".