FBI Director-designate William S. Sessions was admitted to a San Antonio hospital yesterday with a new episode of bleeding from the ulcer that caused him to be hospitalized here last week on the eve of his swearing-in ceremony.

Sessions, 57, was in stable condition yesterday at Methodist Hospital in San Antonio, according to a Federal Bureau of Investigation statement. He had gone home to Texas for a few days of recuperation before the ceremony, which had been rescheduled for Thursday. The statement said it has now been postponed indefinitely.

The FBI said that Sessions' physician, Dr. Richard M. Rubio, said the former federal judge "is believed to have experienced more bleeding, which is not unusual in these cases." The statement said the problem is not life-threatening and that Sessions is not expected to require surgery.

Sessions was admitted to George Washington University Medical Center here last Wednesday night after becoming ill and fainting aboard a jet to Washington. Doctors at George Washington diagnosed bleeding from a small ulcer of the duodenum, the section of small intestine adjoining the stomach.

He was released from the hospital Saturday, and a hospital statement said he had been placed on a regular diet and on medications to reduce stomach acid secretions and promote healing of the ulcer.

A Washington doctor familiar with Sessions' treatment at George Washington said that because the ulcer has not yet had a chance to heal fully, bleeding sometimes recurs in such cases during the first few weeks after the initial episode.