Metro General Manager Richard S. Page yesterday proposed a fiscal 1981 budget that would increase by about 56 percent the amount of money local and state taxpayers would have to provide to run the bus and subway system.

The size of the proposed subsidy increase -- $51.5 million -- surprised Metro board members, who will face the politically touchy task of getting their jurisdictions to cough up additional revenues. The budget -- though it doesn't assume a fare increase -- undoubtedly will generate one next July because Metro has a policy of adjusting fares annually to cope with inflation.

The good news for passengers, though, is that the budget would provide for some additional service and long overdue maintenance, including fixing buses that run without air conditioning and cleaning dirty subway cars. But some of those proposals are almost certain to be trimmed to keep the size of the increase down.

Page's proposal, which must now go through months of hearings before the Metro board and local governments, is a "lean one," he said in his presentation to the board yesterday. Seventy percent of the $54 million increase in operating expenditures, Page said, is a direct result of a staggering increase in the cost of diesel fuel for buses and the guaranteed cost-of-living increases bus drivers and train operators will receive under their labor contract.

A major new element of the local subsidy is the $11.6 million payment Metro must make next year as part of an agreement it signed with the federal government this week to pay off $1 billion in bonds sold for Metro construction.

One of Metro's perennial problems is that it lacks taxing authority to raise revenue. Therefore, operating deficits are made up by local governments, who technically have no legal obligation to do so. Metro has never covered its costs through fares, and under Page's budget would face a total local deficit of $144.2 million next year, up from $92.7 million.

Page is estimating total operating costs of $275.4 million -- a 24 percent increase over the budget that was approved for the fiscal year that started July 1.

It is impossible at this preliminary stage to tell precisely what the budget proposal will do to individual localities as far as tax rates are concerned. However, Metro's total budget will still represent something less than 5 percent of the billions Washington area governments pay annually for schools, police and fire protection and other public services.

Metro board members, usually voluble on every subject, sat in stony silence yesterday as Page presented what he called "the bad news."

Asked after the meeting why they had been so quiet, Metro Board Chairman Jerry A. Moore said, "I think it's just like a right cross to the chin . . . I'm a little stunned."

Prince George's County board member Francis B. Francois said, "Rev. Moore has put it very well. We certainly were aware there were cost problems, but not of this dimension. From the point of view of Prince George's County, we ain't got it." County officials there are trying to budget under a voter-imposed limit on taxes that does not allow for inflation.

"This is a shock, obviously," said Alexandria Mayor Charles Beatley. "However, I'm still a long-term optimist. I don't see any hope for a large metropolitan area with a functioning transit system."

Under Page's budget, fares will cover about half of the cost of operating the subway and about one-third of the cost of operating the buses. Both of those figures are slightly higher than national averages.

In his message to the Metro board, Page wrote that "to finance operating costs beyond those received from the farebox and related revenues, a subregional nonproperty tax revenue source dedicated to public transportation is essential."

Local politicians agree and have been trying to seek authority from the Maryland and Virginia legislatures to impose just such a tax. Those efforts will be renewed in Annapolis and Richmond in January.

Page suggested improving service by adding eight hours of Sunday subway service to bring it up to 16 hours -- the same as Saturdays -- and a greatly improved maintenance effort for both bus and subway equipment.

Further costs are inevitable with the scheduled opening in November 1981 of the Blue Line from Stadium-Armory through the East Capitol Street corridor to Addison Road in Prince George's County.

Maintenance, Page said, has been deferred by Metro to keep costs down and the price of the policy is beginning to show. Page's predecessor, Theodore C. Lutz, knew that maintenance was being deferred and worried about it privately.

"If somebody really doesn't like the size of these numbers," Page said in a special briefing for the press Wednesday, "substantial reductions can be achieved only with reductions in service . . . If somebody says cut $43 million, my answer is, 'Which service do you want to eliminate.'"

Uncontrollable costs -- those that rising prices, labor contracts or federal laws make inevitable -- have been striking hard at Metro, not only in the planning for fiscal 1981 but also for the current fiscal year.

For example, the cost of diesel fuel for Metro has risen in the last year from 46 cents a gallon -- the budgeted figure -- to 68 cents. It is budgeted in fiscal 1981 at an average of 74 cents.

The hourly wage for a bus driver -- the base figure from which the salaries for most unionized Metro employes is figured -- has increased from $8.14 to $9.40 since April 1978. Bus drivers receive guaranteed quarterly salary increases based on the cost of living index; in one quarter this year that meant a 12 percent increase.

The energy crisis has increased Metro's costs in other ways. Since July 1, when the gas lines were long, Metro has added 66 buses to the daily schedule to meet increased demand. Most of those additions have come in the District of Columbia and Fairfax County, and those two jurisdictions are likely to face the largest increases in their Metro subsidy. CAPTION: Graph, Metro's Impact on Local Budgets NOTES: Subsidy includes for the first time $11.6 million interest payment on Metro revenue bonds. Total local subsidies are figured after federal and state aid is deducted. There is no state aid for Virginia jurisdictions. Proposed budget assumes no increase in fares, although an increase is probable; The Washington Post