It depends on the bishop. It is certainly not sinful for a bishop to tell a third party about a confession. I am not aware of many bishops actually turning in anyone to the police. It certainly could happen, especially in cases that involve sexual abuse, but I honestly don’t know how common it is.
It is not uncommon for a bishop to talk to a stake president or other ward leaders about something a person takes to the bishop to discuss privately. When I was LDS, I naively assumed that the bishop was not allowed to divulge anything discussed in his office, but that is not the case.
People confess because they feel guilty or they get ratted out by others. When a Mormon confesses to a bishop, there is no forgiveness of sin. Bishops can mete out penances in certain situations. For certain sins, it goes to the stake level for a disciplinary council where testimony is heard and a group of men decide on the punishment. Forgiveness comes later, sometimes much later, and is often at the whim of the bishop and when he decides the person has been punished enough for the Mormon Heavenly Father to forgive.
