Montgomery County Executive Charles W. Gilchrist proposed a $952 million budget for 1985-86 yesterday that includes a $40 million increase for school and transit programs and could raise the average homeowner's property tax bill by as much as $145.

Gilchrist's budget for the fiscal year that begins July 1 is nearly 8 percent larger than Montgomery's current $883 million spending plan and reflects the executive's emphasis on improving roads, mass transit and other county services in the rapidly growing upcounty area north of Rockville.

"We can't do those things without recognizing they cost money," Gilchrist told reporters at a luncheon marking the start of his final two years in office, after which he plans to study for the Episcopal priesthood.

Gilchrist said that while it may be possible to make small cuts in the property tax rate next year, under his proposal, the owner of a typical $100,000 home will pay $44 to $145 more in property taxes, for an average 5 percent increase over this year. The difference will depend in part on which of the three assessment districts the house is located.

Gilchrist said the increase in tax bills should be no higher than inflation and was justified to defray the cost of expanding government services and construction programs.

Because the 8 percent increase in Gilchrist's budget will exceed the expected inflation rate of 5 percent, the budget must be approved by five County Council members instead of the customary four-vote majority. Gilchrist's 1985-86 budget marks the first time in his six years as county executive that his recommended spending plan has activated the 1978 charter amendment requiring the five-vote majority.

The executive's proposed budget comes as the county embarks on an ambitious six-year plan to build $57 million worth of new school facilities and spend at least that much more to improve highways feeding the long-awaited Red Line extension to Shady Grove, which is scheduled to open in six weeks.

Gilchrist's proposal also will add employes to the county government. He is expected to recommend increasing the 440-employe Ride-On bus staff by 60 persons and accelerate by four months the hiring of 33 recruits to the 777-officer police department.

Some Gilchrist aides said privately yesterday that they expect his budget to face some opposition from school officials, who already are calling for more funds for renovations to lower-county schools than those recommended by Gilchrist.