That is not your responsibility. If its against the law, report it to the authorities, but otherwise it is none of your business, and you should leave it at that.
Confession is the responsibility of the sinner, and when they are ready they will go to the bishop.
What if the person is in a calling and they aren't saying anything. Suppose they're like the Relief Society president or something like that.
I reckon you should just pray for the person with the calling. I know Heavenly Father see's everything and is aware of whats happening and if its really that serious, He will let the Bishop know in his own way. But I strongly believe the sinner should be given the opportunity to confess with out being compelled. That's such an important growing experience on Earth that the sinner shouldn't be robbed of.
We have a responsibility, that if we know someone is engaged in serious sin, to bring it up to our priesthood leaders. However, that is the end of it.
Examples include adultery, drug abuse, child/spouse abuse, etc. There is a list in the Handbook of Instructions of "When a Discipline Council is Mandatory." The list includes apostasy, serious transgression while holding a prominent church position, and pattern of serious transgression (among others).
Well, I am a counselor in the bishopric.
However, I think it is our responsibility to report particularly egregious and/or long-standing sins. If they warrant reporting to law-enforcement, then we should do that first (such as child abuse).
I am not talking about running to tell the bishop when you see someone entering a bar or buying some tobacco. Nor am I talking about reporting that someone is obviously not paying a full tithe, or habitually drives over the speed limit. It is only the very bad, destructive behavior.
I completely agree with Nighthawk, personally I cannot and will not make a blind eye in a situation such as child or spouse abuse, I will report it immediately to local authorities AND Church authorities.