I don't see it as you violated her trust. If I understand it correctly, it's basically like you each have a different standard of what's appropriate to tell a close friend.
Even if now you feel like she's right and your standard was wrong, it just means you were wrong about that specific thing.
It's different than if you realized you were crossing a line that wasn't right to cross. In that case it would be like your intention was to wrong her or you weren't looking out or whatever. In this case it seems more like you just had a different standard about what was appropriate.
I think she could trust you again just by recognizing that you saw it a different way and your intention wasn't to wrong her.
If she was reading your phone without your permission, that seems not so great.