When should I fess up about a mistake I made?

So, my high school band room has a closet that has food that students usually aren't allowed to be in. I am one of the few that is allowed to be in there. For a while, I have been taking food from there. It started out with me taking a snack because I have to eat when I take my medicine. Since then, it's escalated. Recently, my math teacher figured out that I stole some food. She said I have to fess up to my band director. The problem is, I'm one of his "star students" and he trusts very alot. He already ask me if I took stuff from there and I straight up lied and said know. What approach should I take with this?