Mrs. Bush also visited with friends who take care of the White House residence, where she and President George W. Bush lived during his two terms in office from 2001 to 2009.
Trump's relations with the Republican establishment have been rocky since his insurgent campaign took him to the party's nomination and then a shock election win in 2016. The Bushes accompanied the elder Bush's remains to the nation's capital on Monday.
Pelosi and Chuck Schumer, the Senate Democratic leader, placed wreaths in the short ceremony before the rotunda was opened to the public.
Trump also did not attend the funeral in August of another Republican giant, former senator John McCain.
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Bush, who died Friday at the age of 94, will be memorialized on Wednesday at the National Cathedral in Washington.
At the rotunda, U.S. Vice President Mike Pence said there was a kindness about Bush that "was evident to everyone who ever met him".
Dole, who is now 95-years-old and served the state of Kansas in the U.S. House and Senate, faced Bush in the 1988 Republican primary battle for the presidential nomination. "During his presidency, national and world leaders came to Walker's Point to address issues of national and global importance in the peaceful and lovely setting of the ME coast in the summer", he said.
As official Washington paid its respects inside the Capitol, Americans queued up outside the Capitol Visitor Center for their chance.
"It was with sadness that I learned of the death of President George H W Bush last night", her statement read.
Although Bush's funeral services are suffused with the flourishes accorded presidents, by his choice they will not include a formal funeral procession through downtown Washington. "I don't think there are leaders like that today - the World War II generation, especially". Many banks and other businesses also will shut down, and government buildings are flying flags at half-staff until December 30.