When I was growing up there were times when I was troubled but I didn't tell my parents because I wanted to deal with it on my own, and I didn't want to worry them. I was also concerned that if I told them I would lose some of my freedom.
So how do you know? You don't. One of the things you have to accept about being a parent is that you cannot control everything, and you cannot fix everything for your child. Your child won't always want to tell you everything, they are people after all and have their own sense of privacy. If you try to control and fix everything they're likely to resent you, or they won't learn to fix their own problems. This isn't always easy to accept, in fact it's one of the hardest lessons I've had to learn. I knew it conceptually before my kids were born, it's putting it into practice that is the tricky part.
What you have to do as a parent is to form good lines of communication with your kids, give them the skills to deal with situations, and building experiences that will make them confident in themselves. Then bullies won't matter, they'll deal with it on their own.