More than a million people were stranded or inconvenienced yesterday by a strike against the nation's largest bus system, but a union official predicted the walkout would be over quickly.

Earl Clark, president of United Transportation Union, representing about 5,000 drivers, said new talks were held yesterday with the Southern California Rapid Transit District.

The drivers, mechanics and clerks went on strike at 12:01 A.M. Sunday. The state mediation and conciliation service took over the dispute when the strike began.

Clark said he felt the strike could be ended this week.

The RTD, an all-bus system, normally records 1.2 million boardings a day on more than 2,400 buses in Los Angeles, Riverdale, San Bernardino and Orange counties.

The contracts for about 5,000 drivers, 1,200 mechanics and 485 clerks expired May 31. Talks began last April and broke off Saturday.

Much of the load of rider traffic went to private car pools and to Commuter Computer, a private nonprofit company that arranges car pools.

It was the fourth strike against the RTD in seven years.

In addition to wage disputes, the company wants to hire part-time drivers to cut back on overtime now being given drivers. The RTD also wants to use disciplinary measures against drivers who abuse sick leave.