Former president George H.W. Bush and son, former president George W. Bush, watch with family as the coffin of former first lady Barbara Bush is placed in a hearse outside of St. Martin's Episcopal Church following her funeral service on April 21, 2018 in Houston, Texas.
McGrath then tweeted a photo of the socks stating, "The socks worn by the 41st President of the United States at today's funeral for former first lady Barbara Bush".
"It was my honor to travel to Houston to give my respects to Barbara Bush", Melania Trump said in a statement.
A burial will follow at the Bush Library at Texas A&M University, about 100 miles (161 kilometers) northwest of Houston.
Meacham recalled her quick wit that made her so popular.
Bush was remembered as a woman who represented the best of the World War II generation. Eight of her grandsons will serve as pallbearers.
Bush, who died Tuesday aged 92, was wife to the 41st U.S. president and mother to the 43rd.
The Rev. Dr. Russell Jones Levenson, Jr., rector of St. Martin's Episcopal Church, said she was humble, courageous and "tired of waiting on the next chapter".
The motorcade left Houston following a private funeral attended by roughly 1,500 people at the church she and her husband, former President George H.W. Bush, regularly attended.
George H.W. Bush was helped into the cavernous sanctuary with a wheelchair by George W. Bush.
A "VIP reception" hosted by former President George W. Bush is expected to being at 11 a.m. ET, and the funeral service is scheduled to start at 12 p.m. ET.
The former first lady's son Jeb Bush also stepped to the lectern, and shared what his mother most likely would have advised him in delivering his eulogy: "Jeb, keep it short, don't drag this out ... and don't get weepy". In their remarks, Meacham and Baker emphasized Bush's role as a mother and grandmother, with Baker describing her as a "tough but loving enforcer" whose 73-year marriage to her husband was a real-life fairy tale. Susan Garrett Baker, wife of former Secretary of State James Baker, spoke of Bush as a "feisty" friend who managed 29 homes in 17 cities.
The private funeral was held at the St Martin's Episcopal Church here a day after more than 6,000 people paid their respects to the woman known by many as "America's matriarch".
Jeb Bush also recalled asking his mother about death on the last time he was with her- and whether or not she was ready to go. Robin died of leukemia in 1953, just before her fourth birthday. Barbara Bush, who has written multiple books herself, served as honorary chair of the foundation until 2012, when she handed over the reins to her daughter, Dorothy Bush Koch.
First lady Melania Trump was also in attendance at the funeral. According to an aide, Melania brought two members of the White House residence staff as her guests.
And he said she was devoted to her husband - the "only boy she ever kissed".
Mrs. Bush was by all accounts content to be a wife and mother, but mistaking her gentle nature and simple appearance, for anything other than quiet strength was a grave miscalculation.
After she died, Obama and his wife praised Bush "for the generosity she showed to us throughout our time in the White House". Bush met a service member, "She would shake hands, look them straight in the eye, and [say], 'Thank you for your service'".