Many Northern Virginia and Montgomery County travelers using Dulles or National airports will be able to get door-to-door airport limousine and bus service beginning next May.

Under a recently approved Federal Aviation Administration plan designed to make the underutilized Dulles more attractive to residents, a private firm under contract with the FAA will pick up travelers at their homes and shuttle them to new bus terminals along the Capital Beltway and then by bus to the airports.

The exact costs of the service are not yet known, but even the longest trips such as those between Rockville and Dulles would probably cost no more than $10 to $12, well below present taxi fares, according to FAA officials.

The FAA also will buy a new $2.5 million fleet of 14 luxury buses that will run more frequently to downtown Washington and to the new suburban terminals along the beltway--the first two terminals probably near Springfield in Virginia and near the intersection of I-270 and the beltway in Montgomery County. A third terminal is scheduled to be located near the West Falls Church Metro station when it opens in 1985.

The new services will make the two federally run airports more accessible to travelers, reducing the costs and travel time, according to Richard A. Griesbach, manager of business operations for the airports.

At present, airport buses and limousines connect the two airports with downtown Washington, Silver Spring, Bethesda and several Northern Virginia suburbs such as Tysons Corner and Reston.

Travel time between Dulles and the nation's capital, about 40 minutes in non-rush hour, is expected to be cut about 15 minutes when the Dulles Access Road Extension opens this fall, according to FAA travel estimates. During rush hour, travel time will be reduced as much as 30 minutes, FAA officials said. The 3.5-mile extension links I-66, which opened last fall inside the beltway, and the existing 15-mile Dulles Access Road, which now ends at the beltway and Rte. 123.

Airport bus fares almost certainly will drop, said Griesbach, because the private contractor operating the new buses will get them free from the government and thus have lower operating expenses. The current airport bus operator, Airport Limo Inc., charges $7.75 for Dulles trips and $3.25 for those to and from National, rates the FAA said it expects the company may soon ask to increase. Airport Limo operates a fleet of seven or eight buses, according to Griesbach.

The firm is expected to be one of the bidders for the new bus-limousine concession at the airports, which the FAA is now advertising. Congress recently approved the $2.5 million for the new buses in the 1983-84 fiscal budget and the FAA is seeking bids, with delivery slated for this winter. Bids for both must be in by the end of this month.

Plans for the bus purchases were announced more than a year ago, but the FAA had not previously publicized its specific plans for new bus terminals on the beltway or for the door-to-door airport limousine service.

"There is going to be a drastic improvement in transportation to Dulles, both in scope and in quality," Griesbach said, "and this could dramatically help travel at Dulles . . . increasing airport travel by as much as 15-20 percent."