The Metro Board decided yesterday to let the citizens of Fairfax City keep their Metrobus service even though their local government has refused to pay for it and is running competitive buses.

Just coincidentally, the Metrobus service seems to be keeping a significant number of riders off the new Fairfax City buses, which means that Metro is increasing Fairfax City's costs to run the competitive buses.

"We're convinced we're still saving money and there's no question we're operating a bus service people want to use," said Robert Becker, a Fairfax City spokesman.

How is ridership on the city-sponsored buses?

"It's increasing," Becker said, "but I'd have to say not by leaps and bounds."

Metrobus, which has continued to operate its daylong Fairfax City service while the board has been debating the issues, reports that it's still carrying about the same number of riders it always did - an average of 992 a day to and from Fairfax City.

Since Jan. 3, Metrobus has been in direct competition with the rush-hour-only service Fairfax City has chartered for two years from Grey Line. The Grey Line service, according to Becker, has attracted about 340 users a day - or 170 users one way. That is just about half the seating capacity Fairfax City has chartered.

The charter costs Fairfax City $71.75 per trip. Fares collected, on an average load of 24 people, total $26.40. That means the city is subsidizing its new service by $45.35 a trip.

Assuming seven round trips a day, five days a week and 50 work weeks in a year, that amounts out to a total annual subsidy of $158,725 that Fairfax City is picking up right now for its commuter charter.

The Metrobus operating subsidy that Fairfax City finds so offensive totaled about $72,000 in fiscal 1977 and was projected to be $82,000 this fiscal year, with a drop to $62,000 next fiscal year because of shortened bus trips in Virginia due to the opening of the subway.

That is an unfair way to count, Fairfax City's spokesmen have insisted, because it does not include rapidly escalating operating subsidies for the subway. Metro officials, notably Board Chairman Joseph S. Wholey, have said they were willing to negotiate the rail cost issue with Fairfax City and tried to do so without success.

"No such arrangement (excluding Fairfax from rail costs) was ever offered," Becker said.

Fairfax City residents, at a public hearing, asked Metrobus to stay. Northern Virginia's other jurisdictions have agreed, at least for a while, to pick up the cost - and the revenues - from the Fairfax City riders.

"Keep those costs on the books," Wholey told the Metro staff yesterday. "At some point (Fairfax City) might like to rejoin, and we could present them with an outstanding bill."