Just ask her out for a drink/coffee or if you're feeling bold ask her out for dinner.
Try not to come off as sleazy, be respectful and if she says she'd rather not accept it and remain friends.
It really is that easy and it's even easier because you know each other and you don't have to pick up a total stranger. You be amazed how good it feels when you have jumped over yourself in that regard.. no matter the outcome.
Well, yeah, if you want to be all reasonable and level-headed about things.
Well.. don't knock it till you've tried it. I thought similar like you until i got over myself and went for it.. sometimes you strike out and sometimes you don't.
As i said you are halfway there.. there already is sympathy between you so getting a rude turndown is highly unlikely.
If that's you in your avatar i'd say you are also not ugly or repulsive (might think about a new hairstyle though but that's just personal opinion).
All the thinking and research and whatnot you do will not solve your problem.. in this case Nike had it down best when they said "Just do it".