For starters, they are both World War II heroes and they both ran for president in the 1980s, with Bush finally prevailing in 1988.
George HW Bush was remembered just feet away from what he called "Democracy's front porch", the west-facing steps of the Capitol where he was sworn in as president. At the casket's side, an aide helped Dole into a standing position.
During Dole's salute to Bush, the attending crowd remained silent. He was the Republican presidential nominee in 1996.
The remains of former President George H.W. Bush were being taken by train from Houston about 80 miles (130 km) northwest to his presidential library in College Station, Texas, on Thursday, Dec. 6.
Bush's son George W. Bush, the nation's 43rd president, posted the photograph on Instagram, with a message announcing Sully's transfer to Walter Reed National Military Medical Center in suburban Maryland.
James Baker, who served as Bush's secretary of state and was a longtime friend, eulogised the former president as a peacemaker and "a truly lovely human being".
Bush died last week in Houston at age 94.
"He was a man of such great humility", said Alan Simpson, former Republican senator from Wyoming.
Sully assisted Bush, who used a wheelchair, with various tasks following the death of former first lady Barbara Bush in April.
British TV presenter Piers Morgan was also saddened by Bush's passing, chiding Comedy Central's The Daily Show for posting a meme about the awkward meeting between Donald Trump and Barack Obama at "a great man's funeral".
Flags on public buildings are flying at half-staff for 30 days. The yellow labrador's full name is Sully H.W. Bush.
The queen and Philip weren't the only ones who visited with and had a close relationship with George H.W. Bush.
FRENCH CONNECTIONS - Who are the 'gilets jaunes' (yellow vest) protesters?
And on a highway near the southern city of Aubagne, protesters took over a toll booth to let vehicles pass for free. He has refrained from speaking publicly about the protests and has largely remained in his palace residence.