Trust comes back slowly because the other person has to see the change, not just hear about it.

An explanation cannot do this work, however sincere it is. What rebuilds trust is a series of ordinary occasions where the old thing could have happened and did not, observed by the person who was hurt. Talking about how much you have changed often slows it down, because it asks for credit before the evidence exists.

Say less and do the small things on time for a while. Let them find the change rather than presenting it. If you are the one waiting to trust somebody again, you are allowed to take the time you need for that.