Education Secretary William J. Bennett, whose four months in office have been marked by stormy relations with students, college presidents and educational lobbies, has come under sharp attack recently from a new and unexpected quarter: his longtime supporters in the New Right.

In editorial pages and private interviews, conservatives have derided Bennett with the disdain they usually reserve for liberal opponents. Their venom is particularly virulent, they say, because they had considered Bennett to be a friend and ally.

Specifically, they are riled that Bennett forced the resignation of two conservatives who became controversial: Eileen Marie Gardner, who lasted three days as a special assistant for educational philosophy, and Lawrence Uzzell, who had been tapped to spearhead administration tuition tax-credit initiatives.

The two resigned in April after an unusual congressional hearing in which Sen. Lowell P. Weicker Jr. (R-Conn.) attacked their view that federal aid to the handicapped should be eliminated. Weicker, chairman of the subcommittee that oversees the Education Department budget, has a son born with Down's syndrome.

Bennett thought the controversy would end when the two aides resigned. But that was when the attacks from the right began.

"Bennett Cave-In Distresses Conservatives" said a headline in the next week's issue of Human Events, a conservative weekly. The article said Bennett was "knuckling under to a liberal GOP senator's vicious smear campaign."

Bennett "swallowed the distortions" of Eileen Gardner's views, wrote Burton Y. Pines, vice president of the Heritage Foundation, in its Education Update newsletter.

"A McCarthyite smear campaign," raged Gardner herself in a series of public statements. "If Bennett had found my views 'repugnant,' why had he invited me to join his personal staff?"

"We shall see how protective Bennett is of conservatives," wrote Howard Hurwitz, a longtime education columnist, in the May 18 issue of Human Events. "Running from Weicker has not endeared him to conservatives."

In an article headlined "Critics of Aid to Handicapped Are Correct," Hurwitz added that he, too, thinks the handicapped aid program should be abolished -- along with the department that administers it. Hurwitz seemed to dare Bennett to fire him, too, pointing out that he receives a department per diem as a member of the National Advisory Council on Bilingual Education.

"Let him try that business on me," Hurwitz said in a phone interview. He said he had sent a copy of his article to Weicker, adding, "I don't need government handouts . . . . Now it will be interesting to see whether I'm reappointed or not."

The avalanche of criticism is unusual since Bennett was one of the few candidates for the secretary's job who agreed to meet with New Right groups to talk about the job.

For example, after Bennett was nominated last November, the Moral Majority Report, the newsletter of the Rev. Jerry Falwell's group, wrote in an article headlined "Finally, A Friend in Education":

"His President Reagan's appointment of William Bennett as DOE secretary last week was a clear indication the president understands who his friends are. Bennett talked with conservatives consistently during the decision-making process and even met with more than 30 conservative organizations at one particular meeting to discuss his conservative credentials."

So far, Bennett has refused to return the fire. One department source said, "He's frustrated that he has to keep seeing this stuff."

Some conservatives said their outrage is based on more than the resignations of the two aides.

"When Lowell Weicker bellowed, Bill Bennett caved in," said David Sanders, field director for the Conservative Caucus. "If he spends his entire tenure kowtowing to Lowell Weicker, he's not going to get much done. When you make a decision to hire someone , you have to have the intestinal fortitude to stand behind it."

Some sources said the comments reflect the deeper frustration among conservatives over the fact that, five years after Reagan first took office, they still have not achieved their principal goal for the department -- abolishing it.

"Caving in" to Weicker, they said, is just one aspect of what they see as the administration's more general, philosophical "cave-in" on Reagan's 1980 pledge to dismantle the department, which they see as symbolic of the government's big-spending bureaucracies.

Reagan was forced to shelve plans to abolish the department to win Senate approval of Bennett's nomination. In a letter to Sen. Orrin G. Hatch (R-Utah) earlier this year, Reagan said he has "no intention of recommending the abolition of the department . . . at this time."

Bennett, who previously had said he did not think the department should exist, was forced to retreat and accept it as a fait accompli. When asked by Weicker in April whether he thought the department should be abolished, Bennett replied, "I really don't have time to think about it . . . . I can be without a job in this position and I don't think the government would be any worse off."

A study group inside the department is considering ways to reorganize, rather than abolish, the department.

To the right, that about-face is nothing short of treachery. "Bennett believes that the department should be abolished , too," Hurwitz said, "but it's hard to refuse so schmaltzy a job."

Said Sanders, "Conservatives have a new axiom around town: Once we start getting our people in positions of authority, they're not our people anymore."

Recently, Bennett was faced with a headache involving an advisory council on research, whose conservative members had come under attack by moderates and liberals on Capitol Hill. George C. Roche III resigned as chairman of the National Council on Educational Research after Bennett, in effect, closed him out of the decision-making circle.

Bennett made that move to appease congressional critics, who had threatened to hold up the nominations of two other Bennett aides: Gary Bauer, to be undersecretary, and Chester Finn, to be assistant secretary for research.

Still, Bennett retains his liberal critics. The People for the American Way, which monitors issues involving the separation of church and state, issued a "report card" critical of him earlier this month, with the tongue-in-cheek name of "A Department At Risk."

The group criticized Bennett for "staffing the department with far right ideologues opposed to the concept of public education." The report -- apparently oblivious to the latest controversies -- concluded, "Under Bennett, the far right has a new friend at the top."