The White House ordered Education Secretary Terrel H. Bell to cancel at the last minute a speech he planned to give last night at predominantly white Bob Jones University on "Restoring Traditional American Values in the 1980s."

Craig L. Fuller, presidential assistant for Cabinet affairs, told Bell Thursday that it would be improper for him to speak at the fundamentalist college while Bob Jones is fighting in the Supreme Court to overturn an Internal Revenue Service ban on tax exemptions for schools that discriminate. Oral arguments in the case are scheduled for Oct. 12.

In addition to muttering about Bell's political naivete, other White House aides expressed relief that Fuller had ordered the cancellation and averted another firestorm of criticism like that following President Reagan's announcement in January that he would revoke the tax exemption ban. "We don't need to stir that up again," one aide said.

Bell accepted the invitation of the college's president, Bob Jones III, months ago to speak at the Greenville, S.C., school, which has a few blacks among its 6,000 students but forbids them to date or marry whites. Bell had noted the lecture date routinely in a report to the White House, but it was not brought to the attention of Fuller until this week.

Informed of the cancellation while being interviewed by an Associated Press reporter Thursday night, a disappointed Bob Jones III said, "It just leaves us having to cancel a very important occasion that we had looked forward to so greatly."

Jones criticized Reagan's handling of the tax-exemption issue, but had only praise for Bell, whom he called a "fair man and a man of integrity."

"I hope the incident will not hurt Mr. Bell because I think a lot of him and I would not want him to be embarrassed in any way because of us," Jones told the AP reporter.

He declined comment on the matter yesterday, as did Bell, who had special assistant Susan Schonhaut handle reporters' telephone calls. Schonhaut declined to describe the content of Bell's speech, although others who had seen it said nothing controversial was in it.

Schonhaut did say that the reasons for cancelling included concern about Bell's appearance on the campus as the case is pending before the Supreme Court and about the need for Bell to be here to deal with budgetary problems.

An uproar on Capitol Hill, in editorial columns and elsewhere greeted Reagan's announcement Jan. 8 that he was revoking the IRS ban on tax exemptions for Bob Jones University and Goldsboro (N.C.) Christian Schools, a 500-student school that does not admit blacks.

Reagan later told black parochial-school children in Chicago that he had made a mistake. He and others in the administration said the action was taken not for policy reasons, but because they believed the IRS had overstepped its bounds with the ban. Later, Reagan sent legislation to Congress that would ban exemptions for schools that discriminate by race, but members of both parties said it was unnecessary.

Reagan's reversal incensed conservatives and southern fundamentalists who voted for him in 1980. They argued that it was a dispute over freedom of religion, not race.

Reagan spoke at Bob Jones University during his presidential campaign, but feelings there about him have cooled considerably. Jones told the AP reporter, "The Reagan administration has made a lot of problems for us in this case."