Trump, who derided McCain's heroism in Vietnam and prodded the senator even during his illness, was asked by the family to stay away.
Bush died at his Houston home on Friday night, seven months after his wife Barbara died. Such traditions have a long history dating back to Abraham Lincoln's funeral procession, which crossed through 180 cities and seven states on its way from Washington, D.C.to Springfield, Illinois.
He was sent off from his beloved Texas with full military honors at Ellington Field Joint Base Reserve in Houston. After services in Washington, there will be another funeral in Houston on Thursday followed by burial at the Bush Presidential Library in College Station, Texas.
WASHINGTON: America´s national farewell to George H.W. Bush began Monday as the 41st US president embarked from Texas on his final journey to Washington, where his remains will lie in state in the US Capitol rotunda.
"If anybody at anytime knew anything about the 41st president of the United States, they would completely and totally understand that he would welcome the current occupant 100 percent", said an aide in the office of the former president told Politico.
"In death, presidents are measured not only by their accomplishments but by what their tenure says about sitting presidents - and in this case, the contrast appears stark", wrote the Post's Greg Jaffe.
Google muted the bright colors of its logo on Wednesday, to honor George H.W. Bush on the day of his funeral. It's not going to be about anybody else.
"I think he was one of the kindest, most generous men", said Marge Frazier, who visited the downtown statue on Sunday while showing friends from California around.
His son, ex-President George W Bush, will deliver one of the eulogies.
Bill Clinton will be among the living USA presidents to attend, along with dozens of foreign leaders including Germany's Angela Merkel.
A state funeral for Bush will be held in Washington over the next three days, beginning with him lying in state in the U.S. Capitol Rotunda until Wednesday morning.
Trump ordered the federal government closed Wednesday for a national day of mourning.
"George H.W. Bush was a man of the highest character and the best dad a son or daughter could ask for".
Fred Curry, one of the few African-Americans in line, is a registered Democrat from Hyattsville, Maryland, who voted for Bush in 1988, the election won by the one-term president.