With only six of its 100 members on the floor, the Senate took just 15 minutes yesterday to approve its version of the District of Columbia's $1.3-billion budget for the 1979 fiscal year.

Its action, taken by voice vote, sends the measure to a joint Senate-House conference to resolve differences with the House version.

The Senate added about $40 million in spending to the House version while recommending that the federal payment for the city be $238 million, or $26 million below the House figure. The federal payment is designed to compensate the city for its inability to collect taxes on federal and diplomatic property.

Sen. Charles McC. Mathias Jr. (R-Md.), ranking minority member of the D.C. appropriations subcommittee, called the level of the federal payment "too low," but did not propose to increase it.

The budget, Mathias said, "is a lean budget . . . (that) reflects reality. It is the kind of a budget the people of the District of Columbia want . . . Every program recommended by the municipal government has found a place in this bill."

Sen. Patrick J. Leahy (D-Vt.), chairman of the subcommittee, said he would recommend an increase in the federal payment later in the year if city revenues fall short of projections.

Mathias and Senate Majority Leader Robert C. Byrd (D-V.Va.) spent much of the 15 minutes of discussion of the bill praising Leahy for his work on it.