The timetable had the wrong locations listed for four stops and one bus stalled and died in rush-hour traffic, but the inaguration of Fairfax City's independent commuter bus service yesterday attracted 159 riders.

The number was not quite half the number of commuters who normally take Metro buses to get to work in Washington, but city officials were pleased, nevertheless.

"With Metro continuing to run buses in the city, we weren't sure what we'd get," said Robert A. Becker, public information director of the city. "All things considered, everyone is very pleased."

Not everyone outside Fairfax City, however, was as sanguine. Fairfax County Supervisor Joseph Alexander, who is a member of the Metro board, said he was concerned about the success and possible proliferation of systems like Fairfax City's. They skim off the profitable commuter runs and leave Metro with the money-losing runs between rush hours and at night, he said.

"I hope we don't see proliferation," he said, "because if we do, we can forget about a metropolitan bus system."

Fairfax City, an independent city of 21,000 located in the midst of Fairfax County, launched its own bus service after a disagreement with other Northern Virginia jurisdictions over the city's share of Metro operating subsidies.

One of the 159 riders on yesterday's inaugural ride was Karen Stram who recently moved to the city from Antioch College in Ohio to begin a new job in Washington as a paralegal assistant.

"I left in plenty of time to get there by 9:30," she said shortly after boarding the bus - the last of seven chartered from the Gray Line Inc. of Washington - that left at 8 a.m. from the city parking lot on Old Lee Highway (Rte. 237) near Main Street (Rte. 236). The Gray Line bus commuter operation makes stops only in Fairfax City.

But about 15 minutes after the bus departed it stalled on Jermantown Road just short of the intersection with Rte. 50. "It just conked out," said driver Randolph Boone.

After trying repeatedly to get the bus going again, Boone radioed for a replacement, which arrived from the city parking lot in a few minutes.

While Boone and his passengers were transfering, a Metro bus bound for Rosslyn swung around the stalled vehicle, and its driver shouted from his open window, "Tell them to take a real bus next time."

Meanwhile, Thomas Jeschke, who had been the second of six persons who boarded the bus discovered that even if it were on schedule, he wouldn't get to work on time. "I'm going to be a half hour late," he said after studying the schedule.

The bus was due to arrive near his office on Constitution Avenue at 8:55 - 25 minutes after Jeschke, who works for the international operations division of the U.S. Customs Service, was supposed to begin his job.

Jeschke actually ended up getting to his office about 9:15 because of the breakdown on Jermantown Road, Stram did manage to get to her office on K Street on time, despite the delay.

Both he and Stram said they'll give the Fairfax City system a chance, though Jeschke will have to take an earlier bus to get to work on time. The Metro bus that he has taken in the past gets to his destination about seven minutes earlier - primarily because the Fairfax City buses wind around a broad perimeter in the city to reach as many potential passengers as possible.

Metro officials did not count passengers that boarded their system's buses yesterday in Fairfax City, although a spokesman said a check may be made later this week.

Metro makes about 131 trips daily to and from Fairfax City, and about half of those trips occur during the morning and evening commuting hours. Of the 992 passengers that board Metro buses daily in the city, about 645 get on during the commuting hours.

Not all those passengers live in the city. Some are residents of Fairfax and Prince William Counties who drive to the city and take a bus from there. The commission that regulates area transportation fares has forbidden the city from selling tickets to noncity residents. The Fairfax City buses cost $1.10 to and from Washington, 20 cents cheaper than Metro buses.

If the city's buses run at 85 per cent capacity - a much higher rate than yesterday's inaugural - the city would have to provide a subsidy of about $93,500, public affairs director Becker said.

While that is virtually the same amount of what would be the city's share of Metrobus subsidy for fiscal 1979 - $93,200 - Becker said the city would still be saving money because Metro lumps bus and rail subsidy bills together. The city's share of the combined bus and rail subsidy for fiscal 1979 has been estimated at $287,600.