How do I approach this woman?

[Amelia]

MBA next fall. I came across this profile of a Bosnian women that I have never met on facebook. We are both what they call "Liberty Girls" and hardcore Ron Paul fans, that's how I got to know her on FB. She congratulated me several times on my acceptance to Harvard MBA program and we were at the same rallies and CPAC several times but I didn't know her before. I don't know why I'm telling you all this. I'll come to the point.

I've never been in any lesbian relationships before so you couldn't really call me that. I haven't even been in a relationship for 3 big years. But somehow, I like this woman. She is I think 30 or 31 but younger than me. I don't know if this is obsession and it might sound funny but she's on my mind most of the time. I am not sure if she's attracted to me but I am feeling attracted & like to talk to her. She's intelligent, smart and also going to school for an MBA. MY question is: is there any way to ask her out and get to know if she wants what I want? Rejections hurt me but I get over then in week so I'm not worried about getting rejecting, all I want is to ask her out & let this feeling out, you know what I mean? My main worry is the people. She knows the same people I am close friends with so it could hurt my reputation if anything goes wrong.
PS: I posted this on here because nobody would answer on "Dating"

[april sunshine]

Distant relations never works.

[Pick This]

How would you two not working out hurt YOUR reputation? Are you saying people would then know you like women, and it worries you they'll think that you are lesbian? I mean, even if they did think that, so what?

[Universeone]

Stop it.
What do you expect from lesibian relationship !
Judt forget her and find a good guy.