The Metro board indicated yesterday that it would continue in-house management of the region's bus system and reject a bid by an outisde firm to take control of day-to-day bus operations.

The board deferred the final vote for one-week at the request of D.C. Mayor Walter E. Washington. But it was clear that ATE Management and Service Co. has lost in its effort to make Washington the 33d city in which it operates buses.

To win approval under the compact that governs major Metro board decisions, ATE would have needed four yes votes, including at least one yes vote from Virginia, Maryland and the District of Columbia. Each jurisdiction has two votes.

Both Virginia members - Fairfax County Supervisor Joseph Alexander and Arlington County Board Chairman Joseph Wholey - told the Metro board they would vote against ATE.

It also appeared - both from comments at the board meeting and from private interviews later - that only D.C. Council Chairman Sterling Tucker could be counted as a solid ATE vote.

Members cited reasons ranging from the extra cost of contract management to belief that bus services has improved dramatically under new general manager Theodore Lutz to an unwillingness to go aganst Lutz' recommendation as reasons for staying with house management.

Lutz had recommended to the board two weeks ago that management remain with Metro, but also had said that he could live with a decision either way.

Tucker, who recruited Lutz for the general manager's job, told Lutz during an executive session that he was unhappy that Lutz' recommendation "did not seem to be based upon any professional judgment - it was one bus company evaluating another," Tucker confirmed that yesterday.

Lutz walked out of the executive session at that point. He left on a much-postponed vacation the following week and did not attend the board meeting yesterday.

Lutz has been pushing for a decision - any decision - on contract management so he can hire an assistant-general manager to run the transit system. "I have to know whether the assistant will be managing the people we have now or an outside management team," Lutz said. He called his recommendation on the ATE management proposal, "the toughest I have had to make."

Tucker has been a staunch advocate of contract management for some time. He was the chairman of the Metro board on July 3, 1976, when Metro-buses left thousands of Bicentennial fireworks watchers stranded on the Mall of hours. As a result of that transit breakdown, the impetus for contract management was born.

ATE, a aggressive firm that has built a solid reputation for management and marketing in the transit industry, actively sought the Metro contract and contacted some board members including Tucker, ATE president Philip J. Ringo has told The Post.

When Lutz took the job as general manager, he was instructed by the board to seek bids from contractors interested in running the buses.In April, Lutz told the board that ATE had made the only "responsive proposal."

At about the same time, ATE hired the Washington legal firm of Danzansky and Dickey to represent it here. One of the leading attorneys in that effort was Robert Washington, chairman of the D.C. Democratic Central Committee and a close political ally of Tucker.

Tucker said, "I didn't even know when he was hired," when asked if he had recommended Robert Washington to Ringo. Ringo said Danzansky and Dickey was recommended to ATE by other contacts in the District. The fact that Washington knew Tucker was not lost on him, Ringo said, "but that was by no means the determining factor . . . The Metro compact is a complicated legal document and we needed a firm that would give me a sounding board."

Although ATE has an office in Arlington, its headquarters is in Cincinnati.

Ringo all but conceded defeat yesterday while pointing out that the final vote is scheduled for the next week.

In the interim, board members will study the final reams of papers that have been presented by both sides, including proposals for various incentives and performance standards for bus operations.

ATE would have charged Metro about $800,000 a year, but claimed it could save enough money in bus operations to reduce that cost to between nothing and $250,000 annually.

"With rail taking so much of our time, the bus problems are not being reduced in my opinion," Tucker said in an interview. "The people who are running it are the ones who already have failed."