Bush died Friday aged 94 and will be laid to rest Thursday afternoon at his presidential library in College Station, Texas.
Bush spokesman Jim McGrath posted a picture Sunday of the yellow Labrador retriever named Sully with the caption, "Mission complete". Thousands paid their respects at a weekend candlelight vigil at a pond and others contributed to growing flower memorials at Bush statues at the library and a park in downtown Houston.
Baker called him "far and away the best one-term president we have ever had", alluding to Bush's single biggest political failure - his loss in the 1992 election to then-governor Bill Clinton.
Bush's body will lie in state in the Rotunda of the U.S. Capitol from 7:30 p.m. until December 5 at 8:45 a.m., with a guard of honor in attendance.
Trump has said he and wife Melania will attend.
America's farewell to Bush will begin with his remains being flown aboard the presidential Boeing 747 - made available at President Donald Trump's direction - from Houston to Joint Base Andrews, Maryland, on Monday.
Trump declared December 5, as a National Day of Mourning and called on Americans "to assemble on that day in their respective places of worship to pay homage to the memory of President George H.W. Bush".
The casket will then be transported to the cathedral for Wednesday's funeral service - the fourth held there for a former president.
MATT SAYLES APFormer US president George H W Bush had been suffering from a form of Parkinson's before his death
"I invite the people of the world who share our grief to join us in this solemn observance", he said in a December 1 proclamation.
Retired Gen Colin Powell, who as chairman of the joint chiefs of staff was Bush's top military adviser, said Bush was the "perfect American" and should be remembered for "a life of quality, a life of honor, a life of honesty, a life of total concern for the American people".
Shortly before leaving the service, he married his 19-year-old sweetheart, Barbara Pierce, and forged a 73-year union that was the longest presidential marriage in USA history until her death.
"No matter which party you're affiliated with, everybody seemed to say the same things about President Bush", Molina said.
Sully has his own Instagram account; here he is shown "assisting with voting" as Mr Bush cast his ballot in last month's USA presidential mid-term election.
Bush will be buried next to his wife Barbara, who died in April, and their daughter Robin, who died of leukemia at age three.
The 54-year-old mother of two - America's first African American first lady and wife of the first black United States president - is wildly popular at home and overseas, loved for her warm personality, intelligence and women's activism.
At the Group of 20 summit in Argentina, German Chancellor Angela Merkel, who was raised in East Germany, told reporters she likely would never have become her country's leader had Bush not pressed for the nation's reunification in 1990.
- Facebook’s Sandberg admits to snooping on Soros
- Tottenham fan who threw banana skin on pitch at Arsenal is banned
- Putin says Russia, Saudi Arabia to extend OPEC oil pact
- Can Manchester United win the Premier League this season?
- Bush's service dog will go on to help other soldiers
- Manchester City's Gabriel Jesus fails to seize his big chance
- Uefa ready to bring in VAR
- Modric takes the Ballon d'Or from the grip of Cristiano and Messi
- People saw right through Kareem Hunt's apology interview on ESPN
- Captain Marvel's Cosmic New Poster Arrives Ahead Of Fresh Trailer