The cost of a college education is continuing to climb far more rapidly than inflation, according to a new College Board survey. At some of the nation's most prestigious private colleges and universities, the survey indicates, the total four-year cost of a bachelor's degree has reached $75,000.

"It's sobering when you look at these figures," said Kathleen Brouder, director of information for the College Scholarship Service, the financial aid division of the College Board.

Even with financial aid, Brouder said, "it's going to require quite a bit of effort for most families to send their children" to private colleges.

Despite relatively large tuition increases, averaging 8 percent for the coming academic year, private four-year institutions generally say they have had a strong year in student applications and acceptances.

"If you are at a certain perceived level of quality, then you can charge higher tuition and get the students you want," said Mary McKeown, associate director of the finance division of the Maryland State Board of Higher Education. "Maybe if your tuition is at a certain level, you are perceived to be of high quality."

According to the new College Board data, tuition and required fees will rise an average of 6 percent at four-year public colleges and two-year private schools, and by 5 percent at two-year community colleges, where tuitions already are relatively low.

It is the seventh straight year in which college costs have outstripped inflation. The general cost of living, as measured by the Labor Department's consumer price index, rose by 3.7 percent in the last year, although recent price increases have reached an annual rate of more than 5 percent.

The nation's most expensive undergraduate institution is Bennington College, a fine arts school in southern Vermont, whose total annual cost is estimated at $19,400. Other prestigious schools, including the University of Chicago and most Ivy League schools, are charging more than $12,000 in tuition this fall, and estimate their total costs at $18,000 to $19,000.

At Georgetown University, the area's highest-priced college, annual undergraduate tuition will be $10,950 this fall -- up 7.6 percent from the last academic year. Total costs, including room, board and other expenses, will reach slightly more than $17,000.

Tuition will rise at George Washington University by 9.2 percent, to $9,006, and at Catholic University by 8.2 percent, to $8,740. At American University, it will rise 8.2 percent, to $9,744.

Among the public universities, which are heavily subsidized, tuition and fees this fall for state residents will reach $2,366 at the University of Virginia, a 5.7 percent rise, and $1,740 at the University of Maryland, an increase of 8.7 percent.

At the University of the District of Columbia, the area's lowest-priced college, tuition for residents is unchanged at $634 a year after a 28 percent increase last fall. Officials have said they fear another tuition increase would cut enrollment, which has tumbled by about 25 percent since 1979.

By contrast, Harvard University had more applications than ever, even though its bill for tuition, room and board will be $17,100, with total expenses, including travel, books and incidentals, reaching an estimated $18,800.

That means that a student there can expect to pay more than $75,000 for the four years it normally takes to receive a bachelor's degree. The cost of a bachelor's degree at Harvard and other prestigious schools reached $50,000 five years ago, according to the College Board data.

In statements announcing their price increases, universities said they are needed for faculty pay raises and to improve research facilities, libraries and maintenance. Competition for good faculty members has increased.

In addition, many colleges have raised tuition partly in order to finance expanded scholarship programs for the needy.

For several years the college price increases have been strongly criticized by U.S. Education Secretary William J. Bennett.

"There they go again -- and again, and again," Bennett said yesterday after the release of the College Board report. "When will they ever stop?"

Bennett has contended that rises in federal student aid, opposed by the Reagan administration, have helped fuel college cost increases -- a view that has drawn strong rejoinders from spokesmen for college groups. Federal aid programs reached $16 billion this year. Such programs, excluding veterans benefits, cost $12.7 billion during the 1983-84 school year, before Congress voted a significant increase in 1984.

In the new College Board compilation, the average tuition and fees at two-year public colleges nationwide is $687, with total estimated costs for commuters, including living expenses, coming to $3,889.

At public four-year colleges the average tuition will be $1,359, with estimated costs for students who live on campus totalling $5,789.

Among all private four-year colleges, the average tuition is $7,110. Total estimated costs for a student living on campus will be just under $12,000. The figures include many small private colleges, mostly church-related, whose costs remain relatively low.

In the Washington area, one such institution is Columbia Union University in Takoma Park, which is sponsored by the Seventh-day Adventist Church. Its tuition this fall is $6,480 after a modest 4.9 percent increase. Room and board costs -- for vegetarian meals -- will be $2,000.

Nationwide, the average tuition and required fee increases this fall are similar to those of a year ago, although below the double-digit raises imposed from 1980 to 1983.