Its pretty simple, a shot at a relationship IS worth losing her friendship over, or you wouldn't have brought it up.
You basically love this chick, and she's hurting over previous relationship, thats how birds are, break up, hurt, hurt, find new guy, get over it.
Ask her out, if she says no, thats what men need, you get an answer, have an ackward couple weeks, then spot something else that will bang you and fall in love with another woman, end of.
If you don't ask her, you'll pine for her, for ages, and it will get worse and worse, then she'll find someone else and you'll do the jealous "I wish that was me" thing and grow to resent her, at which point the friendship is done anyway.
Don't be a girl, ask her out, best outcome is you end up together and she gets better and you're happy, worst outcome is you get over her pretty sharpish and don't end up the jealous want to be boyfriend then things go back to normal.