The Metro board yesterday formally proposed fare increases for July 1 that would mean a minimum of 5 cents more per subway ride during rush hours and a first-time charge of 10 or 15 cents for riders transferring from subway to bus at Maryland and Virginia Metro stations.

The proposal is scheduled for public hearings around the area late in March. If adopted in its present form, the proposed fare schedule would raise about $4 million in revenue for the combined bus and subway system and thus cut the amount of local subsidy required to keep the system running. The total local subsidy for fiscal 1980 is estimated at $95.4 million.

Under the proposal, there would be no change in fares for District of Columbia bus patrons, except those few who ride the L-1 express from Connecticut Avenue to Capitol Hill during the rush hours. They would pay a 25-cent express surcharge.

There would be a number of changes in suburban bus fares. The basic rush-hour bus fare for riders boarding buses in Maryland or Virginia would increase from 50 cents to 55 cents. Zone charges between the suburbs and the District would increase 5 cents. Thus a rider boarding in either Maryland or Virginia and riding into D.C. would pay 10 cents more than today.

The proposed new charge for transferring from subway to bus would be assessed only in Virginia and Maryland. At Maryland stations, it would cost 10 cents during both rush hour and non-rush hour periods to make the switch.

At Virginia stations, except National Airport, it would cost 15 cents during rush hour to transfer from subway to bus, and 10 cents the rest of the time. There would be no transfer charge at National Airport.

The present prohibition against transferring from bus to subway would remain. A full fare must be paid for both rides in that case.

Rush-hour subway fares would increase for almost everybody from a minimum of 40 cents per rush hour trip to 45 cents per rush hour trip. That minimum price would buy three miles.

Longer trips would be priced at either 9 cents for each additional mile or 10 cents for each additional mile, depending on what the board hears at the public hearings. The present non-rush-hour fare of 50 cents for all trips, regardless of distance, would remain.

Rush-hour is defined by Metro as falling between 6 a.m. and 9:30 a.m. and between 3 p.m. and 6:30 p.m. weekdays