The ringing of bells indicate some important news that will be heard very soon. The bells could also signify the fact that you wish to be irresponsible, especially if the school bell ringing. The bells that ringing in the church signifies the spiritual aspects of your personality. Perhaps you are trying to get to know yourself better. To get more detailed dream interpretation, please also see the meaning of chimes.
Read more about dreaming of Bells ringing in other dream meanings interpretations.