More and more area residents traveling to the business centers of downtown Washington and Arlington are using mass transit and car pools, a report by the Metropolitan Washington Council of Governments shows.

In the three-year period that ended this past May -- before last summer's gasoline crisis -- Metro buses and the subway showed a 13.7 percent increase in ridership to those areas. Much of that increase is directly attributable to the subway's Blue Line, which opened across the Potomac River in 1977.

Metro's own statistics, developed since the gasoline shortage, have pointed to even more dramatic gains this past summer.

The new report was issued by the council's National Capital Region Transportation Planning Board, and is another in a series of annual surveys of how people move around the urban area.

That urban core includes downtown Washington from Capitol Hill to Georgetown and the Arlington County job centers of Rosslyn, Crystal City, the Pentagon and National Airport.

Between 1975 and 1979, almost all of the increase in the number of people traveling to these areas during the morning rush hour occured on mass transit, while there was a decrease in the number of cars entering the areas.

In 1975; 254,500 people used automobiles to go to these areas. That figure increased 1.2 percent to 257,500 by May of this year. The number of people using Metro -- either the bus or the rail system -- increased from 99,-500 to 113,100, the study shows.

Furthermore, the number of automobiles carrying only one person decreased by 4,200 in that period and the number of car pools increased from 54,400 to 56,000. The number of automobiles entering the downtown area thus decreased by 2,600.

Douglas N. Schneider, director of the D.C. Department of Transportation, said yesterday that the report makes it "clear that things are turning around. It shows that the guys who thought up Metro knew what they were doing."

Another indication of the Metro subway's popularity comes in a new statistic on Potomac River crossings.

When the morning rush-hour count was made in spring of 1978, about 28 percent of those crossing the Potomac into downtown used either the bus or subway.

By this year, that figure had risen to 34 percent. Meanwhile, the number of automobiles crossing the Key, Roosevelt, Memorial and 14th Street bridges decreased from 73,996 to 67,078 from 1978 to 1979 -- a drop of 9.3 percent. Ridership on the subway's Blue Line across the Potomac during the morning ush increased from 15,582 to 23,495 -- more than 50 percent.

For the first time,the report listed the number of commuters to the downtown area who use various private bus lines that serve Washington from outlying areas such as Prince William County and Columbia.

About 4,100 people now ride those buses each day to the center of the urban area. Ronald G. Sarros, transportation planner at the Council of Governments, said, "I believe the market for transit in the area is longhaul. New residents in the suburbs are anxious to get bus service."