WHEN Kathleen Dowdey trooped off to Ireland in 1974 to make her first movie (a 26-minute documentary called "The Belfast Reel"), she came close to becoming another casualty of Ireland's latest "troubles." One close shave took place during a cab ride through Belfast. IRA snipers and British soldiers began firing at each other, catching the cab in their crossfire. "Bullets were flying," Dowdey reports, "and all the seasoned Catholics packed into the cab hit the floor while I sat there bolt upright wondering what was going on. 'Get down on the floor' they told me, and I did. The driver floored the accelerator and took off. And we all got out okay."

But the physical perils of being an independent filmmaker seem to bother the 31-year-old Washingtonian much less than the financial and emotional hazards of her career. Nothing gets Dowdey more worked up than the story of her 18-month struggle to raise money for her first full-length film, "A Celtic Trilogy," which began a one-week run on Friday at the Inner Circle theater.

"I put together a 40-page proposal," she says, "and took it everywhere. I tried the NEA, National Geographic, a few film organizations and television networks and an Irish-American foundation. But nobody was interested." Then she turned to individuals. "I hit everybody I know," she says. But her first real break didn't come until Siobhan McKenna, the grande dame of the Irish stage, agreed to do the narration for the documentary, as well as appear in it briefly. "McKenna made the movie investable," Dowdey says. In the end, three investors, all friends of the Dowdey family, put up the $60,000 to make the film.

Dowdey is a tall, dark-haired, fifth-generation Washingtonian from an Irish American family. Her father is a local attorney who, she says, "taught me confidence." It's a good thing to have: Even with three short films and one feature already under her belt, financial rewards are still in the future. She lives "close to the edge," she says, taking on part-time secretarial and waitressing jobs, working in an editing studio for exchange for her use of it, and sleeping on friends' floors on both sides of the Atlantic.

Her "total commitment" to the nomadic life of an independent filmmaker has tested her confidence. "I don't know if you'd call it an obsession," she says of her vocation, "but you do have to make a choice -- you're going to have to live an insecure life and make lots of sacrifices." Filmmaking, she says, is "going to take everything you've got and your personal life gets shot to hell."

"A Celtic Trilogy" is an eccentric melange of documentary and mythology. The movie is set in three of the surviving strongholds of Celtic culture -- Ireland, Brittany and Wales -- and is, says Dowdey, "an attempt to explore on screen the oral traditions of the Celts." The film is sometimes confusing in the unannounced leaps it takes from one area to another -- and frequently from one century to another. But this confusion, Dowdey feels, is in keeping with the Celtic character. "The Celtic people," she says, "refuse to tell you facts -- they tell you stories instead. And the storytellers make a habit of linking their tales with historical fact and of jumping all over the place."

For all its loose ends, "A Celtic Trilogy" demonstrates Dowdey's resourcefulness. After college, she studied filmmaking at the Rhode Island School of Design; and like many independents, she directs her films, does much of the research and writing, and knows how to run a camera and record sound. "I tend to do things to find out if I can do them," she says. One of the things she can do is put together scenes of impressive visual impact. In "A Celtic Trilogy," the footage of a Welsh mining district and of an eerily empty Dublin slaughterhouse is stunning. "I wanted to illuminate the stories in the film," Dowdey explains, warming up to her favorite metaphor, "in the same way the monks illuminated the medieval manuscripts."

In the world of the New Hollywood, where the average movie costs $6 million and the real blockbusters run up tabs of $30 million and more, independently-made films like "A Celtic Trilogy" represent an alternative to the self-indulgent budgets and predictable formulas of the major studios. Independents are beginning to form distribution collectives to get their movies out of museums and libraries and into real theaters. Although the obstacles to commercial success remain formidable, there are signs of hope. Ted Pedas, whose Inner Circle theater has made Washington a good town for independents, reports that "Rockers" (an indepdent film from Jamaica) made $21,500 in one week recently and broke the house record.

Dowdey is not living in Atlanta, where she recently completed a new short, and is planning her next film on tobacco growers. She is relieved and pleased that "A Celtic Trilogy" is finally finished and playing in her hometown. Which is not to say that she's completely satisfied. "I never wanted to finish it," she says. "I could have spent the rest of my life working on it. And, of course, every time I see the film I change it all in my mind. But it's like a painting -- at some point you have to put down the brush and say it's finished."