Baseball Commissioner Peter Ueberroth, who Tuesday bypassed the union and asked all major league players to submit to voluntary drug testing, yesterday bowed to what he called the "overwhelming" desire of the players and said he would work with the union to institute a drug testing program by the time of the World Series.

"A drug testing program will go a long way toward reestablishing the public's confidence in baseball and bring back a good, positive reputation to all the players," Ueberroth said.

Ueberroth had sent letters Tuesday to each of the 650 major leaguers asking they agree to be tested three times a season. Many teams and players said they had no objection to testing, but most of them said it was a matter for the union to decide.

Yesterday, the commissioner said he had sent a letter to Don Fehr, the acting executive director of the players asscciation, asking Fehr to act swiftly and saying, "We should not burden the problem with personal conflicts."

Fehr could not be reached for comment but his assistant, Mark Belanger, said there was still bad feeling on the part of the union because Ueberroth had "tried to go around the union."

"We will collectively bargain about anything, but there are procedures," Belanger said. "He tried to pressure us into doing something once before. But we don't play that way."

Nonetheless, Belanger said, "Regardless of what has happened, we'll say as we have always said: We will listen to anything and we'll collectively bargain over anything. But we will not sign a blank check."

Ueberroth said his appeal to the players had brought agreement on three points:

*"Baseball players want to clean up the image of baseball on an individual basis and refuse to be tarnished by the reputations of a few.

*"They have expressed their belief that a drug testing program is a viable solution to the problem and are willing to cooperate with all segments of baseball to accomplish a drug-free environment in the sport.

*"Their response was equally overwhelming in their desire that the Major League Baseball Players Association represent them in making arrangements for the program."

"I'm very pleased with the response," Ueberroth said. "It is clear the players will support a drug testing program, and I completely understand their desire to work through the players association. I welcome union participation in eliminating the drug cloud over baseball."

Belanger wasn't sure it was so clear. "I don't know how he got that idea (that players would support a testing program) when so many teams haven't even voted," Belanger said. "And they voted to say, 'Take it to the players association.' "

Ueberroth said he asked Barry Rona, counsel for the owners' Player Relations Committee, to meet with the representatives from the players association and try to set up a program by the Oct. 19 start of the World Series. Lee MacPhail, PRC president, and Rona will represent the owners.

The commissioner's request for testing came during cocaine trafficking trials in Pittsburgh in which more than a dozen players were granted immunity in exchange for grand jury and trial testimony against their alleged suppliers.

The second of seven defendants indicted in the investigation was convicted yesterday. Robert (Rav) McCue was found guilty on seven of 13 counts of selling drugs to ex-Pirates Dale Berra and John Milner.