A similar outpouring is anticipated in Washington this week during the state funeral for Bush, who died late on Friday at his home in Houston. The casket will be loaded onto a plane during a departure ceremony scheduled to start at 10:30 a.m. CST and flown to Joint Base Andrews in Maryland.
In Texas, students, staff and visitors have been flocking to Bush's presidential library on the campus of Texas A&M University.
President and Mrs. Bush were frequent guests at Kyle Field along with many other@TAMU athletic venues.
The two-year-old Sully has been at Bush's side since June, just weeks after the death of the president's wife Barbara, to whom he was married for 73 years.
Once Bush lies in state, his casket will be transported by motorcade on Wednesday morning to the National Cathedral, where a state funeral will be held.
Trump has ordered the federal government closed Wednesday for a national day of mourning. The current president gave Bush, a decorated WWII naval aviator who flew several combat missions, a brief salute before the first couple left the Capitol.More news: Russian Soyuz rocket successfully launches three astronauts to ISS
He said Bush's "quality of life had deteriorated a lot" in recent months, but that near the end he was able to talk by phone with his adult children, including former President George W. Bush. Bush will lie in state in the U.S. Capitol Rotunda until Wednesday morning.
The 41st President will be carried to his final rest wearing socks that pay tribute to his lifetime of service, starting as an 18 year-old naval aviator in war.
"To be honest, at one point in history, ' he said, "it would not have been exceptional to have a president who obeyed and appreciated the norms of the American system and of the presidency, who was civil, who was kind to people and who rose above petty squabbles".
The funeral at the Washington National Cathedral, set to be attended by a wide array of former presidents and politicians, including Donald Trump, will last 90 minutes. The Facebook page for the George H.W. Bush Presidential Library and Museum also shared the image. He was denied a second term by Clinton, who would later become a close friend.
"Who would have thought that I would be working with Bill Clinton of all people?" he joked in 2005.
Bush visits a tent camp for natural disaster survivors on the outskirts of Islamabad, Pakistan, in 2006.