The Fairfax County School Board last night named Associate School Superintendent William Burkholder as the interim replacement for Superintendent S. John Davis, who is leaving July 31.

In addition, in one of several moves aimed at trimming the school budget to the level passed by the County Board of Supervisors, the School Board reduced the number of intermediate and high school students who will be eligible for school bus transportation next year.

Under the new rules, intermediate school students will be provided with bus transportation only if they live more than two miles from school, and high school students only if they live more than 21/2 miles away.

The threshold distance for both intermediate and high school students had been 1.5 miles.

The distance for elementary school students was left at one mile.

The change was expected to permit the system to use about 30 fewer bus drivers than the about 650 employed this year. The total savings, including the price of some 100,000 gallons of fuel, was expected to be about $390,000.

It was not immediately known how many of the 83,000 pupils now riding the buses would be affected by the cuts. The County system enrolls about 131,000 students.

The busing cuts and others made last night were designed to pare the school board's budget by the $1.4 million cut from it by the supervisors. The supervisors cut left the school budget at $178.4 million.

In the second largest cut, the school board reduced by about $250,000 the funds intended for new equipment for older schools.

The money had been intended to bring equipment at those schools to the level of the newer schools, and the cut was seen as relatively controversial.

Cuts were also made in funds budgeted for unemployment insurance ($200,000), air-conditioning $150,000), and major maintenance ($145,000).

Burkholder, named as interim successor to Davis, is a 27-year veteran of the county school system who since August 1977 has been serving as associate superintendent for staff operations.

Davis, who had been described by associates as increasingly frustrated in the county superintendent's post he has held for nine years, resigned May 18 to take a job as state superintendent of public instruction.

Board Chairman Rodney F. Page has said that a "wide search" for a new superintendent would begin in June. The search was expected to take several months, with a new permanent superintendent being installed in January.

Burkholder, a native of Bedford, Va., and a former Marine, holds a bachelor of arts degree from Roanoke College and a master's degree in education from the University of Virginia.