What the hell, single for a while now and yet.. ugh!

So, hello LF users, it's been ages! Well, no it hasn't, but sure has been a while since my last time posting here.

So, what's up you ask?
I'll tell you. But first, this is something that's been aching for a while now and I simply don't know what to do about it.

It's been almost 2 years since I broke up with someone. I was the one to make the call and I know for a fact, that my choice was correct. We simply didn't fit together. We did have similar tastes, we had something to talk about, something to laugh about, but when it came down to us as a couple it felt strangely awkward. We couldn't agree on almost anything. It was always either one of us having to compromise with the other or just downright turn one down. We were really different, fundamentally different, we had different views on life, behavior. Well, it was bad. And intimately speaking, we did not fit together either. So yes, that was the right call.
However, this may be my hormones speaking, but I miss her.
I miss her being close to me. For some reason that sensation of her being there was really comforting and whenever I close my eyes and think of her I just get this feeling, that just crushes my soul. Leaving me thinking about why did I break it off with her. I keep asking, wouldn't it have been better to live with compromise than how I'm living now?
Sometimes I feel like I should give her a ring, hear her voice, hear what has she been up to this whole time. But our break up wasn't the prettiest and I think,.. I know she hates my guts.
I want to apologize to her for leaving her, it's a really dumb feeling and I don't know how to fight it.

Finding someone to fill the gap is out of the question.

So, what do you think, how should I go about this?