I don't have an answer for you, but I can relate to your plight. I am tall and women generally consider me good looking, but I still can't cold approach a woman in public. It's like I have this internal narrative that says "you're not the type of guy that does this sort of thing...you're not outgoing...don't approach." So I'm taking baby steps: making more eye contact, smiling, saying hello to women as they pass, etc. I'm also trying to make more small talk with my co-workers and all strangers regardless of gender or age. Believe me, I feel your pain!
I also recite the DJ Bible: inaction leads to more regret than action. In fact that quote reminds me of a time over five years ago when I was travelling alone in Madrid and there was this beautiful blonde sitting alone at a table in this large plaza. I kept waiting to see a guy come and sit next to her, but it didn't happen. To this day (five years later) I still regret not walking up and introducing myself. Even if she had rejected me, I know I would have felt victorious for having the courage to approach.