Last year Elizabeth Drew had lunch in New York with her editor to discuss a story idea, to write about the everyday life of a U.S. senator. "I couldn't help but thinking," she recalled, "it's me, Lizzie Brenner from Cincinnati, having lunch at the Algonquin Hotel with the editor of The New Yorker. . ."

She smiled, that slightly tight smile that is now familiar to many from her appearances on television. Elizabeth Brenner Drew, once of Cincinnati, Ohio, is now of Washington, and for six years has been a Washington correspondent for The New Yorker. She is the author of three books made from her articles, possessor of numerous awards, is soon to receive her fourth honorary doctorate, and appears to be the quintessential successful Washington woman journalist.

That is: smart, dedicated, career-oriented, somewhat prim and ever-so-serious. Never mind that some people complain that her articles are too long and dull; in other quarters they are hailed as detailed and accurae depictions of the processes of power in Washington.

If there was any doubt about her position in this city of journalists, the guest list to the party thrown by her publisher honoring her latest book, "Senator," (the hard-cover product of that lunch at the Algonquin) read like a Who's Who of Washington political prestige: Vice President Walter Mondale, Sen. Edward Kennedy, Robert Strauss (subject of the latest Drew New Yorker profile), half a dozen other senators and representatives (including the subject of the book, John Cluver (D-Iowa), Richard Holbrooke of the State Department, and numerous well-known journalists.

But, while the outside world may think she possesses the kind of ambition that produces a single-minded pursuit of a prestigious goal, she sees her career as a "series of accidents." She does not consider herself ambitious, or driven, but rather the creature of fortune both good and bad.

Certainly she has had both.

Casual inquires that led to jobs with the Atlantic Monthly and a television interview program on the one hand; the suicide of a young husband on the other. Although she says she has no idea what she will be doing two or three years from now, her niche seems assured. At 43, she is well on her way to becoming a Washington institution.

"Senator" is the story of 10 days in Culver's working life. It is typical of Drew's writing for The New Yorker since June 1973, an example of both her faults and her virtues.

The original idea was to examine the question, "What does a senator do all day?" she said, but like much of her work it developed into a more lengthy look at the process of legislation. This fascination with process characterizes most of her journalism: how things get done, why, and the "intersection of human relationships with institutions."

Robert Sherrill, White House correspondent for The Nation, wrote in a review in The New York Times that the book was a "Valentine" for Culver, encumbered with "balloon sentences, floating around on the ceiling, impossible to grab because they lack names and details." He attacked her use of unattributed quotes (a practice by which journalists can often get someone to say something if nobody knows it was he who said it), and her failure to "convince us that John Culver is so important that even the trivia in his life deserve our attention."

At the same time he, as others have, praised its "admirable realism" and "efficient" recreation of the "horse-trading atmosphere of the Senate."

The book is-as are her articles-characterized by a relentless accumulation of detail, of chronologically ordered dissection of small events ot decisions that lead to larger ones, set in an arena of Washington power.

"She's not afraid to be boring," said Nelson Polsby, a political science professor at the University of California and a friend of Drew. "Her main insight is that process and routine matter . . . she's willing to get it right, which sometimes means taking a long time and a lot of details that some people can't get through. But for we in [the academic world] who really should be getting first-hand exposure to the material, her writing is the purest and finest ore we can get."

She chose Culver, she said, because she wanted a Democrat, a moderate, and "I knew he was well-respected by his colleagues." More important, "I knew he had the capacity for stepping back and being reflective."

Other Capitol Hill observers, while agreeing that Culver is one of the better senators, say nonetheless that he is no effective as she portrays him to be, that she glosses over his faults andd overdraws his virtues. Culver himself said he doesn't think the book is about him; "It's about the process."

But there is another reason for choosing a senator that she viewed as an effective one, and it is this reason that seems to arouse Drew's passion.

"I thought it was important to make the point that there are effective peo-who care about the country . . . because of the swidespread and largely justified disillusionment with politics, and because politicians are all we've got. If we give up on them, I don't know what we've got-we've got a choice between a dictatorship, shooting it out or letting politicians mediate . . . It's pretty tough out there in public life; it ought to be tough. When abuses occur, we should say so. But there's a kind of cheap and easy pandering in journalism that plays to the disillusionment, and it could get to the point where it begins to get at the basis of the Republic we've set up."

Her father was in the furniture business in Cincinnati and no, she did't want to be a journalist since she was a child. She didn't know what she wanted to be, she said, and actually didn't even think in career terms. She ended up at Wellesley College, majoring in political science, getting good grades, and then got a job as a secretary for a couple of young architects in Boston. She took courses in typing and speedwriting at night-skills she uses today.

The secretarial job disappeared after a few months because the architects weren't getting enough business, so she walked around Boston looking for a job. "The big thing was to get a secretarial job in publishing," she said. So she knocked at the brown-stone office of the Atlantic Monthly, was politely turned away, but went upstairs to a small firm that published Writer magazine.

"It was a sort of Mom and Pop publishing company," she said. "Run by Abe and Sylvie Burack. That's B-u-r-a-c-k. . ."

After a few years, in which she "learned to write sentences," she moved to Washington to look for a job, inspired dimly by a summer she'd spent as a college intern working for the Democratic Senate Campaign Committee. She knew someone who said the Congressional Quarterly was a good place to work if you had no experience, so she got a job there thinking it would be temporary and pay the rent before she signed on to work in John F. Kennedy's presidential campaign. She stayed at Cq for five years.

She gradually branched out into free-lancing, and from 1967 to 1973 was the Washington editor of the Atlantic Monthly.

In 1964, she married a lawyer, J. Patterson Drew. Six years later, he killed himself by jumping off the Calvert Street bridge at about 10 one morning, 15 minutes after they'd parked downtown and set off for their separate offices.

"You had to pick yourself off the floor and piece yourself back together," she said of that time in her life, speaking carefully and slowly. "When bad things happen to you, you do not feel. You have to feel, so that you can heal and come out the other side, whole and healthy."

One thing she decided at the time was that "there will be nothing to hide about this, and no loss of pride about Pat."

He was a lawyer in private practice, she said, "at a law firm connected with a business organization, and the whole thing collapsed. He took on a great proportion of the strain. Pat was always the strong steady one people leaned on . . . he started to be unable to sleep and went into a suicidal depression. He went from a strong man to a dead man in just a few months . . . We know from studies that if you want to break someone you deprive them of sleep . . ."

Part of picking herself up and piecing herself back together was to work. Friends suggested she try television, "Thirty Minutes With . . ." Now she appears regularly on "Agronsky and Company," and on panel shows like "Meet the Press."

She lives in the Cleveland Park home she shared with her husband. It is immaculately tidy, furnished comfortably in modest good taste. She has, as her old friend Ann Hamilton put it, "an active social life . . . she's oout every night."

Her manner is contained; she bristles only slightly when asked to respond to criticism of her work. She can be acerbic; her friends say hse is also extremely loyal. Writing doen not come easily to her; "sometimes I hate it," she said.

She relies heavily on her close friends, "my board of advisers," she calls them. The writer she says has influenced her most is George Orwell.

"He was someone who tried to bring a clear eye," she said, glancing out at her back yard. "He had a moral base, and he cared about what was ahppening to his country and his world." CAPTION: Picture, Elizabeth Drew, by Harry Naltchayan-The Washington Post