Friend request a perfect stranger on facebook because she caught my eye

Hello, so sorry I haven't posted in a while, but I'll do my best to catch up.

Actually I had a question. So first things first, I'm not really good at meeting people or at being the one who actually starts a conversation but lately on a facebook page I found a girl that is actually pretty funny and interesting, problem is though, I have no idea If she's straight or not, so I thought that maybe cheking her page I would have found something out.
So i tried, but it is obviously private, so I found myself stalling. Now I know that lately asking random people friendship on facebook just to meet them is not so weird anymore I guess, so I was wondering if I should ask her the friendship to get to know her,but I really wouldn't know what to do after that or with what excuse i should actually friend request her.
So I don't know, any suggestions? The only thing I know is that we kinda listen to the same music and we both like tattoos but that's it. And if I find out that she's straight, and with my luck she probably is, what am I supposed to do? I mean, I'd pretty much feel like an idiot.
Basically I'm just sitting here wondering, and maybe this is a really stupid question, but I've never been the one to take the first step so for me it's a big deal, and I'm basically getting paranoid over nothing.

But thanks to anyone who's kind enough to bare with me and give me an answer.

 

I just find it extremely awkward to add someone that you don't know for no reason, so that's the point. I basically have no excuse to get to know her, so why would I ask her? For what reason?
I'm probably overthinking but still, I don't know if I should and what I should actually do if I do.

 

Maybe I didn't really made myself clear. I'm not looking for new friendships by adding random people, she caught my eye, she seems interesting and I would like to know If I can have a chance with her, because for what I've seen she's pretty interesting.

I'm giving it attention because I wanna know her, that's the point, but I still have to figure out if it's a good idea or not. It has nothing to do with meeting people at groups or stuff like that, I could be' interested in her. Hope I explained it better

And I haven't found her picture, she's just on a facebook page that I use and check almost dayly too, but I've never really had the chance to talk to her directly, so I can't say I know her or that we've actually spoken.