The Senate, responding to pressure from some of its new Republican leaders-to-be, joined the House yesterday in voting to bar the Justice Department from seeking court orders for busing to overcome school segregation.

In what antibusing Republicans called a follow-through on the mandate in last week's elections, the Senate voted 42 to 38 -- with 20 senators absent -- to attach the anitbusing rider to a $9.8 billion appropriations bill for the Justice Department and several other federal agencies.

"How long are we going to allow the federal bureaucracy in the Justice Department to torment the little children of America?" asked Sen. Jesse Helms (R-N.C.), who, along with Sen. Strom Thurmond (R-S.C.), the incoming chairman of the Senate Judiciary Committee, led the latest congressional assault on court-ordered busing.

In vain, Sen. Lowell P. Weicker Jr. (R-Conn.) and other opponents of the antibusing move argued that it would be unconstitutional to bar the government from seeking a busing order when no other remedies to end discrimination are available -- a position endorsed by Attorney General Benjamin R. Civiletti.

Weicker, floor leader for the losing forces, said he will seek to kill the appropriations bill when it comes up for final passage Monday. But he added, "I'm probably going to get beaten."

The House also got down to work yesterday, but on a less emotional issue: it passed legislation much sought by the nation's mayors extending revenue sharing for cities and towns.

Under rules for consideration of the Senate bill, no further amendments on the busing issue can be considered, although it appeared that the vote might have swung the other way if more liberal senators had been in attendance.

The House approved the new antibusing language earlier this year, and the Senate voted to go along last September but was sidetracked from completing action on the issue when Weicker tried to nullify the vote and a filibuster by antibusing forces ensued. The bill was then postponed until the post-election session that began on Wednesday.

The appropriations bill, which also includes a previously approved ban on expenditures to enforce President Carter's grain embargo against the Soviet Union, is the first of a half-dozen major money bills that Democratic congressional leaders want to wrap up during the current lame-duck session.

The busing fight may be just a curtain raiser to clashes that the money bills could spawn in the highly politicized atmosphere of the Senate's transition from Democratic to Republican control -- a climate that has already forced some big appropriations bills to be put off until next year.

It was also, according to Weicker, a harbinger of what can be expected from the incoming Senate, which will have a sharply more conservative cast than the current membership. When the new members are sworn in next January, the Senate will have a 53-to-47 Republican edge, instead of the current 59-to-41 Democratic majority.

In previous years, Congress has added riders to appropriations bills banning the Department of Education from threatening to cut off federal funds when school districts balk at desegregation, but it has not previously tied the hands of the Justice Department in civil rights litigation.

After the vote, Weicker said the action -- unless the Senate defeats the appropriations bill or it dies in conference or President Carter vetoes it -- will mean that the Justic Department will have to withdraw from any case in which busing is involved, and most major desegregation cases do involve it. Moreover, he said, the department will be barred from seeking corrective action if a court busing order is being violated.

"I don't see how the law can be enforced without the Justice Department," said Weicker.

In theory at least, the proposal would not ban busing as a remedy for discrimination, nor would it bar the Justice Deparment from seeking other recourse. "It merely limits the remedies which the department may seek by removing its power to seek mandatory busing, a remedy which is rejected by an overwhelming majority of the American people, both black and white," contended Thurmond.

But opponents argued that it would effectively take the government out of the antidiscrimination fight in education, and Helms said it might give some federal judges second thoughts about busing.

"The antibusing rider completely handcuffs the ability of this country's chief law enforcement agency . . . to even bring suit in school discrimination cases," argued Sen. Edward M. Kennedy (D-Mass.). Moreover, Kennedy added, "How long will it be before legislation is before this chamber to remove environmental cases, prisoner petitions, welfare cases or any other type of case from Justice's jurisdiction on the ostensible grounds that the court may issue a particular type of remedy."

Both Helms and Thurmond characterized the election of Ronald Reagan, a busing foe, as president last week as a mandate to end busing for racial reasons.

However, Helms said he doubted that the elections made much of a difference in the actual vote in the Senate, which voted 49-to-42 for essentially the same position last September before the elections.

The only senators who switched positions in voting for the antibusing amendment yesterday were Majority Leader Robert C. Byrd (D-W.V.a) and Sen. David Pryor (D-Ark.). Among Washington-area senators, Harry F. Byrd Jr. Ind.-Va.) and John W. Warner (R-Va.) voted for the amendment and Paul S. Sarbanes (D-Md.) voted against it. Sen. Charles McC. Mathias was not recorded on the vote. An equal number of Democrats and Republicans -- 21 from each side -- voted for the antibusing rider.

Meanwhile, after a meeting at the White House with President Carter, Democratic leaders said they will try in the lame-duck session to finish all appropriations bills except those dealing with foreign aid, legislative operations and the Departments of Labor and Health and Human Services. They said these three money bills are doubtful. hThey said they will still try to pass bills dealing with paperwork controls, fair housing, criminal code revision and cleanup of toxic waste, although Senate Majority Whip Alan Cranston (D-Calif.) said the toxic waste cleanup bill would probably not make it.

In a meeting with Republican leaders from the House and Senate, Reagan transition chief Edwin Meese said Reagan can "accept" the Democratic leaders' decision Wednesday to postpone a tax cut until next year if it means Congress will move ahead with other budget and spending measures. As for the House Budget Committee's decision to incorporate Reagan's promise of a 2 percent spending cut into the 1981 budget resolution, Meese said, "We have no problems with that at all."

Senate Finance Committee Chairman Russell B. Long (D-La.) said he strongly opposed the Democrats' decision to postpone the tax cut but thought it would be "totally futile" to pursue it now. Senate Minority Leader Howard Baker Jr. (R-Tenn.) said, however, that he had "not totally" given up on pushing for a tax cut.