Vice President Bush was criticized by his rivals for the Republican presidential nomination yesterday for refusing to participate in an Oct. 28 debate with the others on public television's "Firing Line."

Bush aides responded that the vice president had offered to appear at two dates in November, but they said Bush, who plans to enter the race formally in mid-October, would not take part in debates before then. "We have consistently said we are concerned about beginning the process too early," said Craig Fuller, the vice president's chief of staff.

Earlier this week, two Bush campaign advisers, former senator Nicholas Brady (R-N.J.) and media consultant Roger Ailes, asked the producer of the program, Warren Steibel, to delay the debate until Nov. 18 or 25. But Steibel said yesterday that the Republican debate already had been delayed twice and that the other Republican candidates refused to change their plans again.

Steibel said the debate will go ahead without Bush on Oct. 28.

The televised debate had earlier been set for Sept. 2 but was delayed at the request of Senate Minority Leader Robert J. Dole (Kan.).

The debate, hosted by conservative commentator William F. Buckley, would be aired on the Public Broadcasting System, as was the July 1 Democratic debate in Houston.

Former Delaware governor Pierre S. (Pete) du Pont IV accused Bush of "political horseplay" and noted that other debates have been held, "but George Bush says its too early to hold a debate."

He added, "The delaying tactics and efforts to manipulate the 'Firing Line' debate by the Bush organization do a tremendous disservice to the Republican Party, which must select a standard-bearer for the 1988 election.

"George Bush has said his loyalty to President Reagan has prevented him from speaking out on the issues," du Pont said. "This silence is no longer a virtue; it is fast becoming a liability for the Republican Party."

John Buckley, press secretary for Rep. Jack Kemp (R-N.Y.), said, "It's not just a question of him {Bush} not being there. He said he would if it were held on Nov. 18. This would mean he wants to start talking about issues and ideas and his vision 3 1/2 months after the debate was initially scheduled for July. Jack Kemp is planning to be at the debate Oct. 28, and we certainly hope that the vice president sees fit to be there.

Referring to the program hosted by his uncle, Buckley said, "It is too bad that the principal broadcast medium for the conservative movement for the past 22 years is not found important enough for George Bush to deign to appear on."

Tim Archy, deputy press secretary for Dole, said "We are there on the 28th. The senator is looking forward to the debate on the 28th, and we'd like to see all the candidates participate on the 28th."

Steibel said he has commitments from the remaining candidates: former senator Paul Laxalt (R-Nev.), television evangelist Marion G. (Pat) Robertson and former secretary of state Alexander M. Haig Jr. Steibel said a site has not been selected, but Houston is a strong possibility.

Fuller, the vice president's chief of staff, said Bush was told of the Oct. 28 date "just before" it was set. He said the vice president's plan was to use October and early November for "announcement and campaign events." He said, "We haven't specifically locked in the schedule for every day in October and November," but "we've indicated Oct. 28 won't work for us."

Fuller said that Bush's senior advisers, Brady and Ailes, were not consulted by Steibel until this week about the Oct. 28 engagement.

"We've had more than 20 invitations for various debates and forums, and we've not received anything in writing for a debate in October from 'Firing Line,' " Fuller said. "We have been willing to discuss the debate with them because the vice president would like to participate."

Bush, the Republican front-runner, has been needled by other candidates, particularly du Pont, for what they have described as his refusal to articulate a vision for the country beyond the policies of the Reagan administration. Bush has said he will lay out his views after announcing his candidacy.