I don't understand why women don't ask men out? If it's because women who have tried it get negative reactions from men, then welcome to a man's world of asking women out!
With respect, I find it confusing that you are clearly a strong, independent woman, but passively wait for a man to make the first move. Just go for it! What have you got to lose?
I'm very happy when a woman makes the first move. It takes guts to do it and I always respect the gesture. It’s very flattering too. It doesn’t happen often but when it has in the past, I have almost always pursued a relationship with the person.