The Metro Board yesterday approved bus and subway fare increases, effective July 1, that will fall heavily on those commuters making the longest transit trips to downtown Washington. The board also approved the inauguration of Sunday subway service, beginning Sept. 2.

The combined service and fare package means that Metro's projected $120 million operating deficit for fiscal 1980 will be reduced by $3.6 million. It also means that a resident of Bowie who takes the bus to the New Carrollton Metro station and rides the subway downtown will pay 45 cents more a day to get to work and back by public transit than he does today.

Metro's fare schedule will continue to be the most complicated in the United States. The one simple thing in it remains unchanged: Midday, nighttime and weekend subway fares will stay at 50 cents for all trips.

There also will be no change in bus fare within the District of Columbia. Fares still will be 50 cents during rush hour and 40 cents the rest of the time.

Everything else will change. The minimum rush-hour subway fare will be increased from 40 cents to 45 cents for three miles; each additional mile will cost 9.5 cents instead of 8.5 cents. Farecard figures out the tariff at the end of the ride.

Suburban rush-hour bus fares will be increased by a minimum of 5 cents, and there will be a 5-cent increase in the zone charge for crossing the District line into either Maryland or Virginia.

The possible fare permutations for commuters who take both bus and subway to work - and about 200,000 people do just that every weekday - are noted in accompanying charts. The Maryland resident who transfers from bus to subway at New Carrollton has the biggest single round-trip fare increase in the system. Most Maryland commuters will pay 25 cents to 35 cents more a day for round-trip transit service.

Increases for most Virginia commuters to downtown will average 15 to 25 cents, depending on where the transfer from bus to subway is made.

Metro will continue its policy of requiring two full fares-in other words, no transfer credit-when a rider goes from bus to subway. However, transfers from subway to bus will be accepted when they are supplemented with a new 10-cent transfer charge, plus appropriate zone charges for transfers made at suburban rail stations.

In the District of Columbia, riders will continue to be permitted to transfer free from subway to bus.

Fares for the elderly and handicapped will be one-half the off-peak fare for bus trips and one-half the rush-hour fare for subway trips not to exceed 50 cents.

A special express bus charge of 25 cents will be added to the L-1 express that runs from Chevy Chase Circle to Capitol Hill.

Parking lot charges at the Landover Metro station will crease from 75 cents to $1 and at the New Carrollton station from 50 cents to 75 cents.

The differences in the fare structure across the area reflect differing philosophies in how much of the public transit cost should be borne by the user and how much be subsidized. Generally, the District of Columbia favors a higher degree of subsidization; Virginia favors the highest possible fares and Maryland falls somewhere in between. Each jursidiction is permitted to determine the level of bus service that will be provided within its boundaries.

The subway, inherently regional, has a mileage-based fare schedule that means the same fare would be charged for the same distance regardless of origin or destination. There is even an exception to this policy, however: Persons using the Minnesota Avenue and Deanwood Metro stations during rush hour get a 10-cent cut in their fares that is subsidized by the District of Columbia and Prince George's County governments.

Metro will continue to sell two-week "Flash Passes," but for the first time they will offer everyday riders genuine savings instead of just convenience.

The Maryland and Virginia passes will continue to be sold for $16 and will contain $6.25 and $5 worth of rail fare, respectively, plus virtually unlimited bus rides. The D.C. base pass, which sells for $10 offers unlimited bus rides and $6 in rail fares, an increase of $1.

Sunday subway service will run between 10 a.m. and 6 p.m. staring Sept. 2. It was approved unanimously as part of the fare package after Prince George's County Council member Francis B. Francois failed in an attempt to separate the questions when his motion to do so died for lack of a second. The District of Columbia had insisted that its approval of fare increases for the subway was contingent upon Sunday service.

"It's important that we go forward unanimously on this," Francois said. "We fought the good fight and we lost." Prince George's County is concerned about the extra cost of providing Sunday subway service at a time when its revenues have been limited by referendum. CAPTION: Table 1, Station-to-Station Rush-Hour Subway Fares, The Washington Post; Table 2, Metrobus Fares, The Washington Post; Table 3, Selected Round Trip Rush Hour Bus-Rail Fares to Metro Center