Greyhound Lines Inc. yesterday announced a multimillion-dollar land swap with developer Morton Bender for the site of its 41-year-old downtown bus terminal.

Under the agreement, Bender will build a new terminal for Greyhound on K Street just north of Union Station. Company officials said the new facility will be twice as big as the current terminal at 11th Street and New York Avenue NW.

In exchange, Bender gains a site across the street from the city's new convention center now under construction in an area of the old downtown that appears on the verge of a major development boom. Land prices in the area have been rising sharply during the last year.

Greyhound gets a larger site nearer its New York Avenue garage and maintenance facilities, and near a freeway and Capitol Hill. In addition to the new terminal, Greyhound receives additional land at the 90 K St. NW site that it may develop. The city will have a voice in how the land is developed, however, since it is in an urban renewal area.

Bender said yesterday that he has no plans yet for the old bus station site at 11th and New York. The 32,000-square-foot tract could be worth between $6.5 million and $19 million, depending on its use. The new site of the Greyhound terminal is zoned for buildings up to 10 stories high and would provide a good location for a hotel, according to one real estate specialist who asked not to be named.

Bender and Greyhound officials are still negotiating the final details of the agreement and would not put a price on either piece of land. They also left open the possibility that, in addition to providing the land and paying for the new terminal, Bender may ante up some cash when arrangements are complete. t

Construction on the new facility is expected to begin within six months and the building is expected to be completed by the end of 1982, said Greyhound chairman Frank L. Nageotte. He announced the land swap at a press conference at which D.C. Mayor Marion Barry said the agreement will be good for both parts of town.

Barry called the land swap "an important aspect of this city's forward thrust" and noted that the new bus terminal will be located in a part of town that over the years has been rather neglected.

"We hope this will be the anchor" for development in the North Capitol area, he said. The new bus terminal, modern and angular in design and with approximately 20 bus bays, will be built on the site of a defunct car sales lot.

Nageotte said it will be a terminal that the company can be proud of "in the most beautiful city in the world.

"At our present location as often have buses backed up for blocks on a Friday waiting to discharge riders," Nageotte said. "We're very excited not just about the prospect of a new facility, but about the fact that it will mean better, faster service to our customers and significant easing of the traffic flow for the downtown area as well."

He added thast the new facility may bring new riders into the area because the new building "may make some people a little more comfortable about using our facilities." He also said that it will provide easier access to commercial shippers who send products via Greyhound.

Greyhound is the largest intercity bus company, in terms of operations, in Washington. It brings approximately a million travelers a year into the area and has some 107 regularly scheduled daily arrivals.

The Continental Trailways terminal site at 12th and I streets NW is reumored also to be for sale but a spokesman would say only that a move in Washington has been under continuous study for some time.

Nageotte said Greybound had been in discussions with Bender, who is chairman of the Blake Construction Co., for approximately five months but that the company had had the move under consideration for longer than that. "People started coming to us," he said.