College expenses will increase by a record 13 to 14 percent this school year, according to a survey released today by the College Board. At more than a dozen East Coast colleges, bills will exceed $11,000.

The survey of 1,160 four-year universities and colleges has been conducted each year since 1970 by the College Scholarship Service, the financial aid division of the College Board, a nonprofit organization representing many U.S. colleges and universities.

Total expenses, including tuition, fees, room and board, books, supplies, transportation and personal expenses, will average $6,885 at private four-year colleges, which enroll about one quarter of U.S. college students. At public four-year schools, the average will be $3,873.

The increases are coming at a time when the Reagan administration's budgetary restraint has somewhat reduced the amount of help that middle-class families can count on from government-guaranteed loans for college expenses.

Under a compromise worked out between the House and Senate, families whose adjusted incomes do not exceed $30,000 will continue to be eligible for loans of $2,500 at subsidized interest rates. For graduate students, the loans can go as high as $5,000. Families whose incomes are more than $30,000 after adjustments for taxes and certain other expenses will also be eligible for some assistance depending on their needs.

Although spokesmen for college and university interests say the final outcome on loan eligibility was better than originally feared, it still means that even parents and students qualifying for help will have to make up the rising costs of education out of their own savings, or find private means of financing.

Students face double-digit increases whether they commute to school or live on campus, and at both private and public colleges, the survey said.

Resident student costs at private colleges will go up an average $803, or 13 percent, this school year. Public college costs will rise 14 percent, or $464 on average, according to the survey.

Tuition and fees will jump an average 13 percent, or $430 at private schools, and $113, or 16 percent, at public colleges.

Since the 1972-73 school year, college bills have doubled. Average total expenses are up by 95 percent at public colleges and 110 percent at private colleges, the report said. The rate of increase in college expenses, however, runs behind the inflation rate. The consumer price index has risen by 123 percent.

This year's higher costs, the biggest increase since the survey began, coupled with the cuts in federal student loan programs "indicates that many parents and students will be asked to cover more of the bill than in the past," said Joe Paul Case of the College Scholarship Service. But Case said the board hoped college prices would moderate next year.

Bennington College, a small, highly competitive Vermont liberal arts college, reported the highest total costs for students in 1981-82 at $12,030.

Twelve other private schools said student expenses will top $11,000 this year: Harvard University and its sister college, Radcliffe, $11,950; Massachusetts Institute of Technology, $11,845; Yale University, $11,600; Sarah Lawrence College, $11,550; Princeton University, $11,289; University of Pennsylvania, $11,200; Brown University, $11,195; Barnard College, $11,150; Tufts University, $11,113; Bard College, $11,063, Dartmouth College, $11,045, and Bryn Mawr College, $11,010.