The Senate Labor Committee yesterday opened its investigation into the administration's handling of Labor Secretary Raymond J. Donovan's nomination with closed-door questioning of FBI executive assistant director Francis (Bud) Mullen.

Mullen, the top FBI official in charge of checking out Donovan's background, testified about two hours before Committee Chairman Orrin G. Hatch (R-Utah) and staff investigators.

Now acting administrator of the Drug Enforcement Administration, Mullen has said that he withheld from the committee last year the fact that Donovan's name had been mentioned in the course of an organized crime wiretap in New York in 1979.

He said he did this because he did not consider it "pertinent" to the pre-confirmation inquiry the bureau was conducting into Donovan's activities as a New Jersey construction company executive.

The Senate voted to confirm Donovan in February, 1981, following stormy committee hearings into allegations that Donovan had ties to a number of gangland figures and members of organized crime.

Donovan denied any such associations, both before the committee last year and in testimony before a federal grand jury this year. A special prosecutor appointed to investigate the allegations, New York lawyer Leon Silverman, announced in June that he not found sufficient "credible evidence" to support any of the charges. But he has since reopened the inquiry after additional allegations came to his attention.

The Labor Committee, meanwhile, voted on July 22 to investigate the performance of the FBI and Reagan transition aides in checking Donovan's credentials. The committee said it had reason to believe that the information it received last year "was incomplete and not provided in a timely manner."

Yesterday's session came after some preliminary dickering with the Justice Department over procedures. It was agreed that a senator would remain present thoughout the questioning.

Mullen had assured the committee last year that the FBI's background investigation had discovered no information reflecting unfavorably on Donovan. He was accompanied at yesterday's session by Robert A. McConnell, assistant attorney general in charge of legislative affairs, and Theodore B. Olson, the Justice Department's legal counsel.

Hatch said Mullen would return this morning for more questioning. The senator said the committee also plans to take testimony from Anthony Adamski, the FBI official in immediate charge of Donovan's background check, and Fred F. Fielding, the Reagan transition team's conflict of interest counsel before assuming his present post as counsel to the president.