"What I did was wrong"
These words have more weight that saying you are sorry. And sometimes it's hard for people to receive an 'I'm sorry' message because it doesn't always show that someone understands the pain they caused.
What these words mean is, you're taking responsibility for the fact that what you did wasn't great and that it caused some damage. They prove that you're not trying to minimize your partner's experience because you understand the relationship between actions and consequences.
"Can you forgive me?"
When someone asks for forgiveness, it's coming from a humble place. There is no pressure to quickly mend the situation because it's literally a request.
In your situation, it will let your partner decide if they're willing to move past what happened or not. You understand that it might take time for everything to get back to normal but, you're willing to wait and ready to face reality if they decide not to forgive you.
"How can I make it up to you?"
No number of 'I'm sorry' can work if there isn't any desire to make restitution. If you've done something wrong, you owe the other person some compensation for any damage done.
This question allows your partner to participate in the restoration processes in a way that they see fit. It can help them relax more and be rightfully entitled to any expectations they have set moving forward.
"It won't happen again"
This type of apology communicates that you have a plan for change and not just seeking reconciliation for the sake of it.
When you say these words, you have to prove it by explaining how you're going to ensure that what happened isn't going to happen again. This is very reassuring and it shows that you're ready to do the work to make things right.