Martha Bowie, a 59-year-old college student who has always wanted a degree and a career, was greeted with a warm hug from one of her 16 grandchildren who came to pick her up after her psychology class at Largo Senior High School last week.

Pursuing a college education is a family affair for Bowie and 19 classmates--the first participants in an unusual inter-institutional undergraduate program for low-income minority women.

The Prince George's County women, all over 35 and 19 of whom are black, are full-time teacher aides in the county public schools, earning between $4,000 and $6,000 a year. They had been unable to earn a college degree in the past for several reasons, including family obligations and financial circumstances.

Bowie, who works with severely handicapped children, will graduate in June 1983 if the two-year program continues. Participants and administrators fear it may not survive proposed Reagan administration budget cuts.

She started college in the early 1960s but didn't have time to finish before she got married and went on to have nine children. But the degree "was always a goal," said Bowie, who wants to teach handicapped children after graduation. She said her husband of 41 years and children are "very supportive" now and that her husband "feels good knowing that the dream that I have always had will probably be a reality in the future."

George Washington University, Prince George's County Community College and the Prince George's County public school system collaborated on the innovative project, which has received $111,780 in federal funds from the Department of Education's Women's Educational Equity Act, according to Rita Ives, chairwoman of the university's Department of Special Education. Each student receives a $3,900 grant, which Ives said covers the cost of course work for one year.

She said the 20 "highly motivated, capable women," some of whom are the sole support of their families, will have earned enough college credits by 1983 to obtain a bachelor's degree from the university in special education and elementary education. They will be certified to teach in either field.

Amy Mazur, the project's field director, added that some of the women have had little or no college course work, while others have had up to 60 hours of liberal arts credits. All were high school graduates, a requirement for their positions as teacher aides in Prince George's schools.

When the project, conceived by Ives and Mazur, was first announced, 153 women expressed in terest and 50 eventually applied. Funds were available for only 20 students, who were chosen on the basis of how completely they met the project's list of criteria.

Ives said interest runs high in the program, with the university receiving calls daily inquiring about it. The courses are also open to and attended by teacher aides who can pay their own tuition.

"We got the . . . institutions together (the university, the college and the school system) and courses were offered when the students could take them," Ives said, explaining the concept. In addition, she said, university and Prince George's college administrators altered existing academic structures "by literally moving the course work into their (the students') back yards." Classes are held at the community college and at nearby Largo High School.

She emphasized that neither the university nor the college lowered its standards for the program and that the women had to meet the same academic requirements as all other undergraduate students. Courses offered include English, history, mathematics, astronomy, physics, geology, anthropology, psychology, economics, political science, government, health, music and art.

Leslie Wolf, director of the Women's Educational Equity Act, a statutory program that makes grants to institutions, individuals and groups such as this one, said the Reagan administration has proposed rescinding the WEEA's $6 million block grant.

Wolf said she thinks this project is "an important model that we hope will be replicated in other parts of the country" and "one that the Reagan administration ought to be pleased about."

Ives said a report documenting the program's results should show that its participants have improved both their self-image and their professional status as they get promoted from aide to teacher, with increased earnings and responsibility.

Rena Jones, 50, an aide at Colmar Manor Elementary School and the mother of three teen-agers, attended college for a year and a half before moving to the Washington area in 1951. A program participant, she said both Ives and Mazur are "efficient and professional" and are "concerned about our problems."

Jones said that without the program she is sure she would not have had any further education "anytime soon."

"I feel good about returning to school, about what I have accomplished and the fact that I have maintained good grades," said Jones. "I thought I was content being a mother and a housewife and that that was the way it was going to go for the rest of my life. Until I got into this program I had no idea of finding myself. I had been out of school for 30 years, but I am taking classes again and I find that this is really what I want to do at this point in my life."

Jones said that she, her husband and her children have had to make sacrifices so she could return to school, but that her family has been "just wonderful."

Jessie R. Clay, 45, an aide at Seat Pleasant High School who entered the program with 48 credit hours, has five children and has been married for 26 years. "I get tired and worn out sometimes," she said. "Last year I was determined to do more work--I felt I had to in order to accomplish my goal. But this year I am taking only two courses."

She said she made straight A's in the teachers' education courses offered by George Washington and has averaged B-plus in the liberal arts courses offered by the community college. Both curriculums are taught at the community college.

"My husband knows I have always wanted my degree," Clay said. "It has always been great with him for me to try. When the children were younger, I really had to push them and I did not have a chance to go back to school. But this time it's a little different. Before, I always did everything for everybody else. I had to learn to do things for myself, be more independent and let some of that go. I am more independent," she added, "and everybody loves it."

Bea Butler, 47, an aide for the last 16 years, had 30 credit hours when she began the program.

"This program is something I really want," she said. "It's hard at times. Sometimes I'm so dragged out. But I can look back now and say, 'Look what I have accomplished.' "