President Reagan's nominee to head the Justice Department's civil rights division said yesterday that congressional efforts to limit jurisdiction of the Supreme Court and ban busing for school desegregation through legislation raises serious constitutional questions.

William Bradford Reynolds, a 39-year-old Washington lawyer, told the Senate Judiciary Committee at his confirmation hearing he was "fully sympathetic with the sentiment" of members of Congress who opposed busing as a remedy in school cases.

But he suggested hearings be held first to build a factual record as to whether busing is "an essential element of a remedial package." Otherwise, such legislation would be vulnerable to constitutional attack, he said.

Reynolds said he didn't know whether he would conclude that proposed anti-busing amendments to the pending Justice Department authorization bill were unconstitutional. Both the House and Senate have passed them.

President Carter vetoed a bill containing such provisions last year, saying it unconstitutionally limited his power to enforce the law. President Reagan said he would have signed it.

Reynolds was stronger in voicing his concern about a proposed bill to prohibit the Supreme Court from hearing cases on school prayer, abortion or desegregation. "In my persnnal view, it's a bad idea for Congress to try to do it," he said. "I have a lot of trouble when one of the three branches of government begins to cut back, modify the powers of another."

Sen. Arlen Specter (R-Pa.), the only committee member besides Chairman Strom Thurmond (R-S.C.) to attend the hearing, made it clear he felt Congress had no business trying to cut court jurisdiction.

Specter also wondered if it wasn't unnecessary to push the anti-busing riders because Attorney General William French Smith already has announced that he wouldn't pursue busing as a remedy in school desegregation cases.

No one showed to testify against Reynolds, who has little record in the civil rights field. He was a Justice attorney during the Nixon administration, arguing cases before the Supreme Court for the department's solicitor general. The committee didn't vote on the nomination yesterday, but Reynolds is expected to be confirmed easily.

As expected, Reynolds took no position on a bill to extend provisions of the Voting Rights Act that require several states to get Justice Department permission before changing voting laws.A House subcommittee has held extensive hearings and is preparing to mark up the bill, but the administration has yet to testify on it.

On other issues, Reynolds testified:

Affirmative action should be part of a remedy in discrimination cases, but defined its application narrowly, as has Smith, to persons who actually suffered injury.

One of his first duties if confirmed would be to review four school desegregation suits the department field in the last days of the Carter administration. In answer to a question from Thurmond, who had requested the review, he said he wouldn't hesitate to drop the cases, including one against Charleston, S.C., if he didn't consider them valid.

He would use the provisions of the Institutionalized Persons Act to try to remedy "inhumane and egregious conditions" in prisons, but felt the primary responsibility for correcting problems rested with state and local governments. The Reagan Justice Department already has moved to placate state officials who have complained about the department's handling of prison cases.

He would examine pending higher education desegregation cases by the same principles used in last week's settlement between the Department of Education and North Carolina.