Do things happen with Bishops? Yes, but very, very rarely. Instead mothers would be better to worry about
relatives, neighbors, your other children's friends, sleepovers, your daughters friends, the internet, (and I hesitate even saying this - the girl's father) more than a Bishop. Having been a Bishop - there are much riskier things to worry about than Bishops. Most parents have no clue all the things their kids get involved with.
I have 4 daughters. I get the concern. I'm very paranoid with them. However, I've rubbed shoulders with and gotten to know dozens of Bishops over the last several decades. They are fine, fine men. They generally are the best the Lord has in the wards. I've been privy to Bishops and Stake Disciplinary Councils so I know some of the things that most members aren't privy to. Our Bishops, in general, are not who we need to worry about.
If you have concerns - just ask if they will crack the door open and let you be in a position where you can see the door. If we get to the point where we can't trust our Bishops - then we are in very sad shape.