The Senate Judiciary Committee finished questioning Attorney General-designate Griffin B. Bell yesterday but gave no indication of when it will vote on confirming the controversial Atlanta lawyer.

Chairman James O. Eastland (D-Miss.) said only that the committee would be "in recess" until he reconvenes it. As of last night, committee sources said, Eastland had not said when that might be.

Some committee members said they hoped that the vote on Bell might take place today. But, they added the committee first will have to act on a request by Clarence Mitchell, Washington director of the NAACP that further testimony against Bell be heard.

However, after five days of testimony from Bell and his foes and supporters, the expectation is that the committee and then the full Senate will vote to confirm him.

In his appearance yesterday, Bell urged the committee to complete action on his nomination quickly. He noted that outgoing Attorney General Edward H. Levi and Deputy Attorney General Harold R. Tyler Jr. are anxious to leave and said, "Somebody's got to run the Justice Department."

Bell added that if he has not been approved by the committee by the time that President-elect Jimmy Carter is inaugurated Thursday, direction of the Justice Department probably would have to be taken over temporarily by outgoing Solicitor General Robert H. Bork.

Bell also said that he plans to resign today from three private clubs in Georgia that discriminate against blacks and women. His membership in the clubs was a major source of the controversy surrounding his nomination.

However, Bell refused to say that he wouldn't rejoin the clubs after leaving the government. He said: "I'll decide then. These clubs may not discriminate anymore."

He also told the committee somewhat heatedly, "I'm flat resigning. There are no ifs, ands or buts about that. Now you want me to say I won't ever be a member of a private club again. I don't want to say that.

"I've done more than most public officials have done. I don't know of anyone who's ever had to agree to what they would do for the rest of their lives just to hold a government job."