You may have noticed that I've been avoiding you for the last {amount of time}. I'd like to apologize for that. I can tell that it hurt your feelings, and it was incredibly childish of me to keep you in the dark and not tell you what was going on.
Basically, I've been avoiding you because {reason}. I was doing a bad job of processing it, and I didn't feel like I could talk about. However, I see now that that just made you feel crummy and bewildered, which I don't want for you. If you can forgive me, I'd really like to talk it out with you now.
Sincerely,
{Name}
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