I want to say sorry to my ex. When should I do it? After one month or as soon as I can?

It's been 8 days since the break up and neither of us has contacted each other. He said he wanted to break up because he was confused. He just started college and he's going to a different school. So he's starting this new episode in his life with new friends, new pressures and new expectations. At first, he asked for a break. I was so emotionally dependent on him at that time so I said no because I thought we already weren't spending enough time together. He then told me that he wanted to experience the college life-- basically getting drunk and sleeping around. But also dating someone who's convenient. That was what really did me in. On the day of the break up, he said he still loves me. That this is just part of the movie where the guy has to do something stupid so that he learns from his mistakes and grows up a bit and try again with the girl he lost. Of course, I was a wreck. I was angry so I did the most hurtful thing I can (slapping him really hard in public and then walking away) as a final gesture to be superior. Since then, I've been working hard to pick myself up. I've cried it all out. I've talked to family and friends. I got myself busy and allowed myself to have fun for myself. Like everyone else who has ever loved, I really thought about what went wrong in the relationship. I'm his first girlfriend and first everything sexually. So I get his curiosity. I also realised that I was being so inconsiderate the first place, because he asked for space for the first time in the one year we've been together and I couldn't even give him that. So now, all I want to do is apologise via email. I want say sorry for the nasty break up and for not giving him the space he asked for. I want to say that he's right, the space is good for us and that I'm doing fine and I hope he's okay too. I just really want to say sorry asap because I did have a fault. Of course I'm still hoping to try again but right now, saying sorry is more important to me.
I want to say sorry to my ex. When should I do it? After one month or as soon as I can?
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