As a BS, I would say that this is a very good letter. You are coming across a truly open and transparent. It is so much better to her it from the WS than by some other means. You have explained what you did and the nature of it and some of the why. That is a really good start. It is clear that this as an ONS and not an LTA and that is easier to handle for a BS (I think).
I am very much a reading writing person rather than a talking person, so this approach would have worked for me. Not everyone is the same. You will need to think whether your BS is a reading writing person too.
One thing I would say is don't read it out to him. Let him read it himself. It will give him time to react and process. Also don't send it out of the blue. Ideally, I think you need to do this face to face. Tell him that you have something difficult to tell him, you are very very sorry. It will be very difficult for him, but it is the right thing to do to tell him. Then give him the letter. Tell him that you will let him read it and then you will answer any questions he might have. Let him read it on his own - leave the room, make a coffee etc.
Then come back an be prepared for the reaction. Be prepared to anger any questions he has. He might rage and storm, try to keep as calm as possible. Tell him you love him, you regret what you did. Say sorry lots of times, tell him you love him lots of times. Hug him if he wants, back off if he wants. You will need to be led by him.
Read How to Help Your Spouse Heal from Your Affair. It will help you.
Thank you for doing this. I so wish my FWH had done the same. The truth has trickled out over years. It turns out that My FWH was and ONS in a car, but he didn't tell me that for 2 years after the first confession. I thought it was much more. For me an ONS is easier to handle than an emotional attachment.
I think your BS will want to know who the AP was. If it was someone he knew or who you still see, that will make it more difficult for him. If it was a genuine one--off that will be easier. If it was someone you both know, you must go into NC and you must commit to that completely.
Delicate question, but have you checked for STDs? If yes, and you are clear, that is another reassurance you could give your BS.
Well done and good luck. It is the beginning of a tough time for you, but you are following the right path and doing the right thing.