He was also a U.S. congressman from Texas, ambassador to the United Nations, chairman of the Republican National Committee, head of the U.S. Liaison Office in China, director of the Central Intelligence Agency and a decorated World War II Navy pilot who flew 58 missions in the Pacific.
During Dole's salute to Bush, the attending crowd remained silent. Bush died last week at the age of 94 at his home in Texas after years of failing health.
Bush will lie in state until Wednesday morning.
President Donald Trump has declared December 5 as a National Day of Mourning. The pair quickly bonded, with the former president even buying socks in honor of his beloved companion.
The Honor Guard carries the casket of former president George Herbert Walker Bush down the center isle following a memorial ceremony at the National Cathedral in Washington, Dec. 5, 2018. They paused steps from Bush's casket for a minute, with Trump saluting and Melania Trump placing her hand over her heart, before they quietly walked away.
The late Mr Bush called Mr Trump a "blowhard".
U.S. Postal Service to shut down on Wednesday for National Day of Mourning
His wife, Elizabeth, is also very close with the Bush family, and served as a Republican senator from North Carolina for several years.
Although Mr 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.
After services in Washington, Bush's remains will be returned to Houston to lie in repose at St. Martin's Episcopal Church before burial Thursday at his family plot on the presidential library grounds at Texas A&M University in College Station.
The New York Stock Exchange will also be closed on Wednesday.
Flags on public buildings are flying at half-staff for 30 days. Here's more on just how well the Prince of Wales actually knew George H.W. Bush.