He was born in Houston, Texas, and died in San Francisco, California on his eightieth birthday.

In late 1943, he was a 25-year old army veteran looking for work. A position as the Senate correspondent for United Press soon provided Drury not only with gainful employment, but also with the opportunity "to be of some slight assistance in making my fellow countrymen better acquainted with their Congress and particularly their Senate."

In addition to fulfilling his duties as a reporter, Drury also kept a journal of his views of the Senate and individual senators. Drury freely offered his first impressions of many senators: "Alben Barkley, the Majority Leader, acts like a man who is working awfully hard and awfully earnestly at a job he doesn't particularly like."

He considered Minority Leader Robert Taft "one of the strongest and ablest men here," and felt that "Guy Gillette of Iowa and Hugh Butler of Nebraska vie for the title of Most Senatorial. Both are model solons, white-haired, dignified, every inch the glamorous statesmen."

Harry Truman was featured as his position changed from junior senator from Missouri to vice president to president in the course of Drury's narrative. Given the period it covered, it is natural that Drury’s diary devoted considerable attention to President Franklin D. Roosevelt and his contentious relations with the Senate. Drury wrote: "If he appears in a critical light, that is because this is how we saw him from the Hill."

In addition to the chamber's personalities, Drury's journal captured the events, large and small, of the 78th and 79th Congresses. He characterized this period as "the days of the War Senate on its way to becoming the Peace Senate."

At times the events Drury described had a national impact, such as FDR's death or the Senate's consideration of the United Nations Charter. In other cases, the effects were felt more clearly within the Senate community, such as the resignation of Majority Leader Barkley, the Senate's rejection of a congressional expense allowance, or the death of Secretary of the Senate Edwin Halsey.

Although written in the mid-1940s, Drury's diary was not published until 1963. A Senate Journal found an audience in part because of the great success of Advise and Consent, Drury's 1959 novel about the Senate's consideration of the nomination of a controversial individual as Secretary of State. With the subsequent publication of Drury's diary, readers could look for clues about the identity of the fictional senators Drury depicted in his novel (which was made into a film in 1962). The book was partly inspired by the suicide of Wyoming Senator Lester C. Hunt.

Drury followed Advise and Consent with several sequels. A Shade of Difference is set a year after Advise and Consent. Drury then turned his attention to the next presidential election after those events with Capable of Honor and Preserve and Protect. He then wrote two alternate sequels to these (the difference being which politician survived an assassination attack at a joint appearance), Come Nineveh, Come Tyre and The Promise of Joy.

In 1970, Drury published The Throne of Saturn, a science fiction novel about the first attempt at sending a manned mission to Mars. He dedicated the work "To the US Astronauts and those who help them fly." Political characters in the book are archetypal rather than comfortably human. The book carries a strong anti-leftist/anti-communist flavor. The book has a lot to say about interference in the space program by leftist Americans.