Hey Shadix!

It's not unacceptable for a man to approach a woman! Who told you that? As long as it's in a non-threatening and NON CREEPY manner. After all, you wont know if you don't try, right? I think what hardcore feminists are trying to say is that you shouldn't approach a random women with obvious intentions of sleeping with her. It makes us women feel uncomfortable. I dont like when guys come on too strong. It irritates me.

Just because she doesnt always say hi doesnt necessarily mean she's ignoring you. And just because she's nice to you, does not mean she's flirting with you.

If you want to get to know her, then there's no harm in asking her out. You can ask her if she would like to have dinner with you sometime. If she says yes, then get her number so you guys can plan a date. If she says no, for whatever reason and with whatever excuse, then dont push it any further.

Hope this helps!