She is just 15, but the slight girl with the punk-rock haircut has been on her own for three years, working her way from Northern California to Northeast Washington by waiting tables and sweeping streets.

She recounted her odyssey recently, sitting in the high-ceiling, sparsely furnished living room of the Sasha Bruce House for runaways on Capitol Hill.

"My father was always telling me to grow up, grow up. Sometimes I think I've grown up too fast," she said after recalling her mother's three marriages and the bitter family quarrel that led her to Washington in search of an older sister. She asked that her name not be used.

More and more teens like this one are crisscrossing the country and traveling over unprecedented distances, according to Deborah Shore, executive director of Sasha Bruce Youthworks Inc., parent agency of the runaway home, and many are ending up on the streets of the District.

"We're seeing a lot more kids who are victims of the economy; their parents just can't afford to keep them anymore," Shore said. "Unlike the sixties, when kids ran away in search of some kind of counterculture, we're getting kids who actually have no home to run away from."

Founded in l977 and named for the late daughter of former ambassador David K.E. Bruce, the Sasha Bruce House recently moved from a nearby row house to the larger four-story home at l022 Maryland Ave. NE. Shore said the move was necessary to accommodate a growing number of homeless teen-agers who often need more long-term lodging.

"We get a lot of stowaways," Shore said. "Kids take the bus or the train up from Florida or down from New York. They get as far as Washington, and then they're out on the street."

Sasha Bruce House is funded by the U.S. Department of Health and Human Services, the United Way, private contributors and, this year for the first time, the D.C. Department of Human Services. The shelter can accommodate 15 youths, each of whom costs about $30 a day to feed, house and counsel.

To enhance community support for the shelter, Shore and Project Coordinator Dennis McKinney have invited 1,500 city government officials, community leaders and parents to an open house May 11 at the home.

The Bruce house is not the only city facility seeing an increase in runaways. Robert Middleton, chief of intake services at the DHS Family Services Division, said his department has counseled eight runaways in the past three months, twice the total number in l982.

"The economy has taken a toll on many families," Middleton said. "A lot of people are holding down two jobs and just don't have the patience for a kid who wants to stay out until two in the morning. Teen-age unemployment is high. . . . A lot of kids say they are a burden, that their parents don't want them anymore."

Interagency cooperation is necessary, McKinney said, because of a growing number of local teens whose parents are homeless too. Without the shelter, many of these teens would end up on the street or in jail.

One such case is Wayne, a Southeast Washington l7-year-old who spent 10 weeks on the street before a friend told him about the Bruce house. His mother, Wayne said, had told him to "get out of the house" when he was 10.

Wayne was subsequently tossed back and forth between two aunts--"one nice aunt and one mean aunt," he said--until the "nice" aunt returned home to find him "stoned" on a tranquilizer commonly known as PCP.

"I blew it with the nice aunt, so here I am," he said. Before the Bruce house he had lived two weeks in an abandoned trailer, then two weeks at a girlfriend's house. The girl's family then tired of Wayne and returned him to the street, where he stayed until the April chill drove him indoors.

"We see a lot more kids in the winter than in the summer," said Shore, whose yearly quest for funding requires her to keep exhaustive intake statistics. The "average stay here is 14 days, but in cases like Wayne's, it can be a lot longer--maybe months," she said.

The statistic that most alarms her is the number of out-of-town runaways--five out of 23 last month, three out of 21 in February.

McKinney said, "We get them from Canada, North Carolina, New York, New Jersey; many of these kids don't even know where their parents are."

He remembers one 17-year-old girl whose mother and four younger siblings had been put up in a temporary shelter, awaiting resettlement aid from DHS. McKinney said the mother told him there was simply no room for the oldest child.

DHS arranged for the family to move to another apartment, but the mother then explained to Sasha Bruce workers that she was simply not interested in caring for her oldest daughter. Ultimately, the mother "disappeared" and the girl was placed in a foster home.

In some cases, Shore explained, a couple of phone calls can patch up an argument and return a child safely home. Of the 73 teens Sasha Bruce sheltered in the first quarter of l983, 40 returned home and only three are still on the run. The rest ended up with friends or relatives, in foster homes or community residences.

Shore and McKinney are trying to persuade police to refer runaways directly to their shelter. Capt. David Bostrom of the police Youth Division said the D.C. Code prohibits such referrals on grounds they violate client confidentiality.

"The police won't make direct referrals to an agency like ours, and they are usually reluctant to involve a runaway in the court system," Shore said. "So they often take the kid back to his family, where the problem started in the first place, and he's back on the street within 24 hours."