Bush often sported bright socks, sometimes with loud, unusual patterns.
Social media users thanked Sully for his services and commented on his and dogs' loyalty generally towards their owners.
The 41st USA president's body is scheduled to lie in state there from Monday to Wednesday.
Trump has ordered the federal government to close on Wednesday and both the New York Stock Exchange and Nasdaq will be closed in observance. His body will be transported by motorcade to St. Martin's Episcopal Church, where he and his wife regularly worshiped. A guard of honor will be in attendance, and the public will be allowed into the Capitol from 7:30 p.m. Monday until 8:45 a.m. Wednesday. Other Bush family members are expected to be at the Maryland military base for the arrival.
My grandfather was the greatest man I ever knew.
H.W. Bush will be honored at several public and private events in Houston and Washington before his burial on Thursday in Texas.
Bush's casket will arrive to College Station from Houston by train on December 6, according to ABC-affiliate KXXV.
A ceremony will be held at the train station as Bush's casket is loaded onto a Union Pacific train.
Following the week of services, Bush will be laid to rest on his presidential library grounds at Texas A&M University, where his wife and Robin, his daughter who died of leukemia in 1953, are buried. And beyond personality, the conflicting presidencies underscore just how little remains today of the Grand Old Party that Bush once led. We will cherish their time with us forever. The crew has been tasked by President Trump with carrying out "Special Air Mission 41".
Bush's eldest son, former President George W. Bush, posted an Instagram photo of Sully lying in front of his old master's casket on Sunday.
The funeral train will include UP No. 4141 George Bush Locomotive, which was unveiled October 18, 2005, during a ceremony near the library and museum on the Texas A&M University campus.
Bush died at 94 on Friday.
Ceremonies at the presidential library will include a missing man formation flyover.
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.