The Fairfax County Board of Supervisors approved a plan yesterday for a jitney loop bus service to run between Vienna, the Tysons Corner Shopping Center and the Westpark-Westgate office complexes.

The bus service, which is expected to cost the county about $72,000 a year, will also run a lunchtime shuttle between Tysons Corner and Westpark-Westgate for office workers who want to eat lunch and shop in the mall.

The Tysons Corner area is one of the most congested in the county, according to Donald Keith, resident engineering the Virginia Department of Highways and Transportation, Keith said he welcomed the jitney bus service "because every little bit will help" relieve traffic jams that often cause long delays.

The supervisors yesterday mentioned the need to relieve the noontime traffice "mess" at Tysons Corner as a major reason for supporting the bus system.

Shiva K. Pant, director of transportation for the County, said yesterday it will take between six and eight months to hire a private firm to run the bus service and to come up with a bus route.

The jitney service, which was proposed by the Northern Virginia Transportation Commission and which is not intended for rush-hour commuters, will not replace Metrobus service in the area.It is intended to reduce severe traffic congestion, especially at noontime, in the Tysons Corner area.

Pant said bus fare will probably be 25 cents and that buses will move on the loop between Vienna and Tysons Corner every 30 minutes. On the lunchtime shuttle, which will operate between 11:30 a.m. and 2:30 p.m., buses will be available every 15 minutes, Pant said.

The bus route between Vienna and Tysons Corner, which will operate between 10 a.m. and 10 p.m. on weekdays and 10 a.m. and 6 p.m. on Saturdays, will not make regular stops, according to a memo given to the board yesterday. Instead, the memo says the buses "would be hailed in much the same manner as one hails a taxicab."

The county is not yet committed to support of the bus system, Pant said. That commitment will come when the board approves a detailed plan for a fixed bus route and a contract with a private bus company.

In 1976, Vienna had a private bus system that failed after one year of operation. That system carried about 120 riders a day, Pant said.

The board approved the bus system yesterday on a 7-l vote, with Supervisor Audrey Moore (D-Annandale) voting no and Supervisor James M. Scott (D-Providence) absent.