Why is Parris reluctant to tell anyone that Betty may be bewitched?

There are several reasons.  First, as a minister, how would it look to his congregation if his daughter is bewitched?  Second, his standing in the community is tenuous.  Some, like John Proctor, have stopped going to church services because of their dislike for him.  He doesn't want to give others more reasons to stop attending.  Remember too that he was not the first choice for minister, Mr. Putnam wanted someone else, so he does not have the most support from the Salem community.  He is also the third minister (I believe) in a rather short period of time.  So again he is not overly anxious to give the townspeople reason to turn against him.  Third, he is worried that people will start a witch hunt and bring in Mr. Hale, thereby taking away some of his authority.