Break Up & Divorce

Guys, How can I gain back his trust?

My ex and I were talking, with the possibility of getting back together in the future, I (F 28) did something that made my ex (M 32) say that he no longer trusts me because I two stepped with someone (we both agreed while dating dancing is romantic and we didn't want to dance with others) since we broke up even though I did it once and stopped and do not plan on going back. I told him about it because I didn't want to feel as though I was hiding anything. He also now doubts my feelings for him because of this. He is moving out of state soon, as he had already planned on. What are some practical things I could do to rebuild his trust and get him to see that that was an honest mistake and to believe me (he has trust issues in general)?
He feels like my words and actions are not aligning in this situation because I told him I thought dancing was romantic when we were dating but when we are broken up I danced with someone (then stopped because I realized I didn't want to be doing that) and then tried to get back with him.
He said he needs space right now so I want to respect his need for space and not talking right now. But I want to fix it and move forward, being more consistent in the future and hopefully get back together but can't show him that if I don't interact with him.

Guys, How can I gain back his trust?
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