The Department of Interior has awarded a $604,000 grant to help buy and develop Northern Virginia's scenic, 42-mile bicycle and hiking trail, which will run from Alexandria to the Blue Ridge Mountains.

The grant, which is part of the Interior Department rails-to-trails program, will allow the Northern Virginia Regional Park Authority to open more than 5 miles of the new trail by next spring. That part of the trail runs along the abandoned Washington and Old Dominion Railroad right-of-way, from the Arlington County line through the town of Vienna. A short section in Falls Church already has been completed.

Virginia is one of 10 states receive part of the $5 million in the rails-to-trails program, designed to convert abandoned railroad rights-of-way, particularly those near urban areas, into open space for recreation or conservation. More than 135 grant requests, totaling $70 million, were received by the Interior Department.

Maryland is to receive $450,000 for a 20-mile section of the old North Central Railroad, which will be used for a multipurpose trail in Baltimore County.

The Northern Virginia grant will speed development of the old 42-mile W&OD right-of-way and permit construction of the paved, landscaped bike trail through Vienna instead of just to the eastern edge of the town, according to Darrell Winslow, executive director of the Regional Park Authority. West of Vienna to the trail's end in Purcellville in Loudoun County, a horseback riding trail will run inside of the 100-foot right of way, parallel to the bike trail.

Plans for two of the three major highway crossings between Falls Church and Vienna have been completed, with a special bicycle bridge to be built soon over the Beltway (I-495) and a wider-than-normal street bridge (Virginia Avenue) for hikers and bikers over I-66 now under construction between the Beltway and Route 7. Construction bids for the Beltway bridge will be opened May 16 by the Virginia Department of Highways and Transportation, with construction to be completed within 120 days after a contract is awarded in June.

The only other major road crossing is heavily traveled Route 123 (Maple Avenue) in Vienna. The state Highway Department has assigned a traffic specialist to work with the Park Authority in determining the safest way to get bikers and hikers across the four-lane road as well as other streets the trail must cross.

The old W&OD railroad station in Vienna will be leased to the Northern Virginia Model Railroad Club as a public railroad museum, Winslow said. Club members have just finished restoring the building.

The Regional Park Authority expects to complete the $3.5-million purchase and development of the entire bike trail by 1982.