The US president has clashed in the past with Mr Bush, America's 41st president who died aged 94 on Friday, and his son George W Bush, the 43rd president who did not vote for Mr Trump in the 2016 election.
Before serving as president from 1989 to 1993, Bush was vice president under Ronald Reagan.
Yet one individual, who shall go unnamed, dared to criticize Sully on the internet because she did not believe the dog's six months of service to the former president was enough to merit our attention.
Flags on public buildings are flying at half-staff for 30 days. "The Bush family's active participation in the Kennebunkport community has touched many lives". Bush, a Navy pilot, survived a bail-out from his stricken aircraft over the Pacific and an earlier crash landing.
Shortly before leaving the service, he married 19-year-old Barbara Pierce, and forged the longest presidential marriage in U.S. history.
Mr Bush enrolled at Yale University after military service, becoming a scholar-athlete and captaining the baseball team to two College World Series before graduating Phi Beta Kappa after just two-and-a-half years.
Sully will have two co-workers in the role, service dogs Sgt. Dillon and Sgt. Truman. He was a familiar presence in Washington: a congressman in the late 1960s, then Central Intelligence Agency director, envoy to China and Republican Party chairman.
"Who would have thought that I would be working with Bill Clinton of all people?" he joked in 2005. 'I was proud to be his leader in the Senate because I liked what he stood for.