She was rummaging through her briefcase, waiting for the New York-to-Washington shuttle, when The Perfect Man walked into the airport lounge.

He had Robert Redford's face and Nick Nolte's body. Gorgeous. A hunk. Adonis in a three-piece suit. She vowed to date him or die trying.

She boarded the plane first and saved him a seat. A slim, head-turning brunette, she wasn't surprised when he seemed about to join her. But he passed her by and took a seat in the rear.

When the plane landed he headed toward the baggage area.Although she had no baggage, she followed. She watched him pick up his suitcase, walk out of the airport and out of her life.

"I figured I had nothing to lose," recalls the 30-ish woman executive. She caught up to him, tapped his shoulder and said, "Excuse me, but I've wanted to meet you and I didn't know how. Can I buy you a drink?

"He said, 'Sure, I'm glad you asked.' We had a wild, fabulous time and became great friends."

From this experience came the rule that has brightened -- for this woman and others -- many a Saturday night: "When in doubt, ask him out."

Washington women live by this motto, claims Rozanne Weissman, who teaches on Open University course on the social scene called The Washington Connection.

"All single women in this town ask men out," she contends, "or they probably don't date at all. It's a competitive place. If you don't ask a man out, chances are someone else will."

"Women aren't waiting for a white knight to carry them away anymore," adds a Maryland psychologist. "They're just as likely to gallop up to him."

A logical reason for this phenomenon could, of course, be Leap Year -- in less liberated days the only acceptable time for woman as wooer -- but in recent years women have been asking men out, regardless of the leap legend.

"If you're a high-powered attractive woman, many men are afraid to ask you out," says a 38-year-old attorney. "They automatically assume you're going with someone or not available. If you don't give them a little encouragement, you'll both wind up sitting home."

"Everyone's so busy that it's tough to meet people," adds Anita Guttenberg, 28, a real-estate specialist. "Often women just have to make the first move."

"Married men are the only ones doing any asking these days," sighs a 25-year-old teacher. "If you want to date a single man, you've got to approach him."

It beats sitting at home waiting for the phone to ring, says Leslie Atkins, 25, a writer and public-relations consultant.

"When I'm the one doing the asking I'm more in control. Then he's the one waiting by the phone. And I figure why not ask out a man I want to date, rather than waste my time with some of the men who ask me out."

Women say men are flattered by the advance. Men who've been asked out agree.

"They're ususally surprised and delighted," says a 30-ish divorcee. "And since they haven't had much practice at saying 'no,' you're usually assured of a date."

"It's an ego trip for the guy," says Richard Haddad, a founder of the men's liberation group Free Men. "It's simply nice to know that someone finds you interesting, likes you and is attracted to your body."

"There are probably men out there who would feel threatened and not know what to do if a woman asked them out," adds Free Men member Dick Conoboy. "But I think most men love it. It really takes the edge off the dating game."

Summoning the nerve to ask a man out "takes a great deal of courage," admits one frequent asker. "It gives you an excellent understanding of what men go through."

Fear of rejection is the strongest deterrent, says Terry Batt -- "I've been single longer than God" -- teacher of an Open University class on the mating game called Making Contact.

"Women for ages have softened the rejection by telling men that they have to stay home and wash their hair or entertain cousins from out-of-town.

"So if a man says he has to baby-sit his cat instead of going out, it gets you in the pit of the stomach. All you can do is take a deep breath, realize you can't be everyone's cup of tea and try again."

"My self-image crupled when I called a man who I thought really liked me and he said 'Janet Who?'" recalls public-relations specialist Janet Gordon, 23. "But if you don't take risks, you never get anywhere."

The first few times might be tough, admits Mary Lee Zetter, 31, a psychotherapist who "made the first move" to kiss the man she later proposed to and is now her husband. "But the more you ask men out the easier -- and the more fun -- it gets."

Asking men out is easier for younger women more used to new roles, says Sharon Austin, 24. She used the technique of asking men over to study when she attended Howard University.

"It's easier for older women," counters a recently remarried divorcee. "When you're over 40 you no longer think it's the end of the world if he says no."

But for any woman, "It's worth it," says Candi Kaplan, a 30-year-old insurance planner who during Leap Year 1976 popped the question to the man who is now her husband.

"Just remember how much more fun it is to be going out than sitting home. Then just blurt it out."