The Metro Transit Authority voted yesterday to start a morning rush-hour bus service from the South west Mall to Farragut Square so District of Coulumbia residents will not have to ride the subway and pay an extra fare.

The shuttle bus, numbered M7, will begin operations Monday morning. It will save D.C. residents who choose to use it at least 40 cents a day because they can transfer free from bus to bus. There is no transfer from bus to subway, and a second full fare must be paid.

There will be no shuttle bus in the evening because riders can transfer free from the subway to the bus.

The decision to reinstate bus service paralleling the subway line is a classic example of politician greasing the squeaky wheel. Anacostia residents discovered Aug. that their express buses to Farragut Square had been terminated at the L'Enfant Plaza Metro station as part of the realignment of the bus system to turn it into a subway feeder.

They complained. The fact that their complaint was heard was evident yesterday by the presence of Mayor Walter E. Washington at the Metro Board meeting. Although he is a member of the board, it was Washington's first appearance there since Nov. 4, 1976, according to Metro minutes.

D.C. City Council Chairman Sterling Tucker was also there, but he regularly attends Metro board meetings. Both Tucker and Washington are considered likely candidates for mayor next year, although neither has announced ward eight Council member Wilhelmina Rolark and some of her supporters also attended. Television reporters, who rarely cover Metro meetings, were also there.

Commuters from across the region have been forced to transfer from bus to subway and pay a second fare. But because of Metro's byzantine bus fare structure, the total round trip cost for Maryland and Virginia residents was about the same as a bus-only trip before the subway. For D.C. residents the cost increased 40 cents.

The decision to start the morning bus shuttle was reached at a meeting of a Metro board committee with the arcane name of Revenue Operations and Subsidy Allocation. Members call it ROSA, for short.

The committee meeting started at 8 a.m. D.C. transportation director Douglas Schneider outlined the problem and the shuttle-bus solution. Tucker spoke of the need to take action. Washington arrived at 8:42 a.m.

Committee Chairman Joseph Wholey, of Arlington County, wanted assurances that the District of Columbia would pay the cost of operating the extra buses.

Tucker provided such assurances, but told Wholey, "I regard this not as a D.C. problem: I regard this is as a systems problem."

The big systems problem is that the subway fares, unlike the bus fares are regional in nature. Anything that takes people out of the subway costs everybody - not just the District - money.

The committee, and finally the board, agreed to try the shuttle for awhile, study the results and solve the cost problem later. It also agreed, perhaps more significantly, to take a serious look at bus operations for the entire Anacostia area, which has been poorly served.

Later in the day, when the board agreed not to run subway service for Redskins football games, Mayor Washington terminated the discussion by saying, "I don't want to talk about the Redskins until I can get my people in from Anacostia."