Audrey Scott, a short, curly haired blond of 44, spends time at home in her walnut-paneled kitchen, cooking, washing dishes, cleaning the table.

But when the phone rings, her kitchen becomes headquarters for the chief problem solver for the town of Bowie, the state's third-largest municipality. About 30 times a day, Mayor Scott is called on to assist her 45,000 constituents who think of her first when school buses are late, when there are power outages and broken water mains.

"For $5,000 a year, 80 hours a week, I get all the harassment and problems of the world I can use, but I love every minute of it," said Scott, who has been mayor of Bowie since 1976.

She and her husband John, an engineer with the Defense Department, live with their four sons aged 17, 16, 14 and 12 in a comfortable suburban home just off Rte. 197.

After five years as chairman of the Bowie Hospital Board, which was charged with getting certification and funding for the proposed public hospital in Bowie, Scott decided to run for a state legislative seat in 1974.

With the help of friends she made through women's organizations and the hospital board, Scott put together a city-wide organization that brought her a fourth place finish in a race to fill three legislative seats.

Thereafter, the plot moved swiftly. With city elections coming up in the spring, she put her well-oiled campaign organization into gear and captured a City Council seat. Heartened by her council victory, Scott ran for mayor the following year against a veteran council member who had finished the last half of the previous mayor's two-year term.

"I decided after a while that if I was going to spend so much time on council work, I might as well be mayor," she now says, laughing. She won a landslide victory against the incumbent and has been reelected twice.

Scott has just completed a term as the Maryland Municipal League's second woman president.

"I think the key to my success has been that I've been accessible and visible," said Scott.

However, her affiliation with the Republican Party in hostile Democratic territory has slowed her climb up the political ladder to a possible congressional seat. Twice she has run and twice she has lost as a Republican candidate for the state legislature.

"I could never be a Democrat," says Scott. "It runs against my principles. I'm a fiscal conservative and I believe that the best government is the government that governs least."

As for her relations with the all-male City Council, she says, "We spend a lot of time together and they respect me. They call me sir, so I guess I'm considered one of the boys."