According to a confidential Yale report obtained by The Washington Post, Princeton staffers logged onto Bush's online acceptance notice four times in one afternoon.
The online acceptance notice for Ara Parseghian, the grandson of the Notre Dame University football coach, also was accessed by Princeton, according to the report.
Yale's Web site allowed undergraduate applicants to see if they were accepted to the university by using their Social Security numbers and birth dates.
Princeton, which looked at the admissions decisions for 11 Yale applicants, gained access to the Web site using information from students who had applied to both schools.
Stephen LeMenager, Princeton's associate dean and director of admission, has acknowledged improperly entering the site, but said he checked it simply to test its security.
LeMenager has been placed on paid administrative leave, and is the only person Princeton has cited in the case so far, Princeton spokeswoman Marilyn Marks said Saturday.
An attorney hired by Princeton arrived on campus Friday to begin an inquiry into whether other staffers were involved.
Marks would not comment on the Washington Post report.
"I cannot comment about individual students or applications," she said. "I know that we do intend to reach out to the (affected) students and I believe that that process has started."
Yale officials did not immediately return calls for comment Saturday.
On Thursday, Yale notified the FBI about 18 unauthorized log-ins to their Web site that were traced back to computers at Princeton, including computers in the admissions office.
The FBI was investigating whether there was a federal violation.
Education experts told the Post a lesson may be that the fierce competition between elite Ivy League universities for top students has finally gone too far, sparking the kind of lapse in judgment that is certain to bring renewed scrutiny to the college admission process.
"In this game, the top colleges all want to land the same students right now -- they want to win," Alvin Sanoff, former managing editor of U.S. News and World Report's annual guide to colleges, is quoted by the Post as saying. "It has never been more competitive on either end, for students competing to get in and schools trying to land the best students."
Nowhere is that competition more strenuous than at Yale and Princeton, two of the nation's wealthiest universities. For years, they have battled over many of the same high school seniors, using financial aid and admissions reforms to lure the most attractive applicants, the Post points out.
This year, Yale admitted only 13 percent of its applicants, while Princeton accepted 11 percent. The two universities began jostling over financial aid packages last year, after Princeton announced a reform that all but wiped out student loans in favor of direct grants. Yale followed with its own dramatic plan.
More recently, reports the Post, Yale developed the first online admissions notification system, the network Princeton is alleged to have broken into.