Education Secretary William J. Bennett told a congressional panel yesterday that proposed cuts in college student aid may hurt some small, high-priced private institutions that rely heavily on tuition, but he said most schools are financially healthier now because of the economic recovery under the Reagan administration.

"I expect we might see, under these proposals, some movement," Bennett told the House Appropriations subcommittee that oversees his department's budget. "I don't think such movement will be dramatic."

The heads of some private universities have said that the new budget proposals -- contained in a compromise between the White House and Senate leaders -- would cripple private education. At issue, they say, is a plan to assume $8,000 as the maximum annual cost of a college education, and to subtract from that a certain amount that the family is expected to contribute, before deciding how much federal money a student is eligible to receive.

Many private universities charge more than $8,000 a year. One critic, New York University President John Brademas, a former Democratic congressman from Indiana, has called the $8,000 proposal "another attempt to drive a wedge between the public and independent sectors" of higher education.

Bennett said at yesterday's hearing that small private schools could survive by more aggressively soliciting gifts from donors. "These institutions did not come into being with -- nor did they have to rely on -- the advent of the federal government," he said.

As for larger, better-endowed private schools, Bennett repeated his contention that "endowments have increased dramatically, thanks to the economic recovery."

Also at the hearing, officials said the Education Department intends to release $75 million this year for school desegregation, even though the administration has proposed eliminating the aid program.

Forty-three senators had signed a letter to Bennett, accusing the administration of "unnecessary" delay in drafting rules to implement the program.

Gary L. Bauer, a deputy undersecretary who has been nominated to the post of undersecretary, told the hearing that the delay resulted from processing comments that have been received, and was not a deliberate attempt to withhold the money until Congress decides whether to abolish the program.

"We are committed to get those funds out in a timely manner and not impound the money," he said.

The money was approved by Congress last year to implement the magnet-school program, which brings together children from differing social, racial and economic backgrounds in magnet, or model, schools. Some school districts, such as Prince George's County, rely on magnet schools to implement voluntary or court-ordered desegregation plans.