"We're going to heaven", Baker said.
"They've always been very special to us", she said.
After a speech from Vice President Mike Pence, Bush will lie in state in the US Capitol from Monday evening until Wednesday morning, under the watchful gaze of an around-the-clock honor guard.
A statue of former U.S. president George H.W. Bush with flowers stands near downtown in Houston on Suday.More news: Trump Imposes Six Month Deadline On Congress For NAFTA Substitute
A formation of Navy sailors and Air Force personnel stood at attention as the plane touched down. From there, a funeral train transports Bush to Texas A&M University in College Station, Texas, the site of the George H.W. Bush Presidential Library and Museum, where he will be laid to rest.
President Donald Trump and his wife later paid their respects, saluting Bush. The federal government will also be closed. USA bond and options markets were also due to be closed, with energy and foreign exchange markets expected to remain open. "Bush of course was defeated for re-election and most people at the time considered him a failed president" because of a recession during his time in the White House. A photo of the two-year-old yellow lab lying next to Bush's American flag-draped casket went viral on Sunday, and subsequent investigations into Sully confirmed that he is ridiculously loyal and sweet.
Mr Bush's spokesman, Jim McGrath, tweeted a picture of Sully with the casket, with the caption: "Mission complete".
Sully is from the nonprofit organization America's VetDogs in Smithtown.More news: Pickford error hands Liverpool derby day victory
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.
His casket was being transported to Washington on Monday for a state funeral later this week. "George H.W. Bush was a man of the highest character and the best dad a son or daughter could ask for".
The motorcade then traveled to Ellington Field.
Memorial services began Monday to honor the late President George H.W. Bush. Bush Sr. loved the dog so much that he even got a pair of socks to honor Sully.
Bush often sported bright socks, sometimes with loud, unusual patterns.More news: Oil prices surge on trade war truce, prospects for Russian output cuts