Mr. Bush has been lying in repose at St. Martin's Episcopal Church, where his family worshipped.
"Then it became silent staring time", Colbert joked as he showed Trump beside the former Presidents, not speaking.
The funeral service began at 10 a.m. local time on Thursday, with more than a thousand people in attendance, according to The Associated Press.
George P. Bush, the former president's grandson and the only member of the political dynasty still holding elected office, as Texas land commissioner, subsequently struck a more personal tone with the man he and the younger generations called "gampy".
He will be interred at the George H.W. Bush Presidential Library Center in College Station, Texas, next to his wife, who died in April, and their daughter Robin who died of leukemia at age three.
The awkwardness of the warring front row was painfully evident
"Bush did not endorse Trump in the 2016 presidential election but sent him a letter in January 2017 saying he would not be able to attend his inauguration because of health concerns, but wishing him the best".
The group had been friends with Bush since they played at a White House barbecue when Bush was vice president. The Obamas shook the Trumps' hands and Michelle Obama told the president, "good morning". Bush was a Navy pilot who was shot down during World War II.
"I think it's just a vehicle for them, Shannon, to be able to contrast what they think Trump is versus the way they're telling us Bush was", Limbaugh said. "And Trump might have half-expected, if not outright welcomed, such a rejection, as it would have given him an opening to abrasively tweet about the Bush legacy, employing Trump's patented Twitter formula: insulting nickname, distracting punctuation, malapropism, logical fallacy, self-own, hit send". While the congregation, including the Obamas and Clintons, read along with the Apostle's Creed, Trump stayed silent.
Trump ordered the federal government closed Wednesday for a national day of mourning.
Brit Hume weighed in Wednesday on Rush Limbaugh's contention that the media's praise for George H.W. Bush after his death has been "phony". Flags on public buildings are flying at half-staff for 30 days.
"I'm just here to pay my respects", said Jane Hernandez, a retired physician in the heavily Democratic city and suburbs.