The important admission that the Director makes is that he once went with a girl to the Reservation and that something happened and the girl got lost.
Right in this chapter, the admission only has a little bit of an effect on Bernard. He sympathizes with the Director and the Director, for whatever reason, gets really angry at him. He threatens Bernard. This actually makes Bernard feel pretty good. It makes him feel as if he has really accomplished something and that he is a true rebel.
If you are talking about how it affects Bernard over the course of the book, then you need to think about how this admission is what leads Bernard to, eventually, find out about Linda and John. It leads to him being able to use them in a variety of ways.