The book of Proverbs says that a brother offended is harder to be one than a citadel. It's like trying to climb the walls of a great, massive, fortified city. And sometimes we do offend others, and sometimes others offend us.
And so in the realm of regaining someone's trust, I think a top priority has to be in humility, in letting that person know that you do accept responsibility for what you did. that you are truly sorrowful, not just feeling sorry for yourself, but feeling sorrowful that you brought hurt into their lives. And then acknowledge that it may take some time to build trust with them.
And in some circumstances, there may be a situation in which that trust will never be regained. Trust and forgiveness are not the same thing. And so you have to trust the Lord that he will make all things right. As one of my mentors said many years ago, There are some things that will just simply have to be resolved in the halls of heaven. And you have to let that be okay. You treat that person with dignity, with kindness, and with love. And whatever trust they choose to extend to you is really ultimately their business.