how to get to know her? i'd appreciate good advice, specially shy girls point of view?

How old are you guys? Do you sit by her on the bus? If you don't, just try sitting by her and making casual conversation. Trust me, we shy girls like guys to be the one to initiate conversation, it doesn't make us uncomfortable whatsoever, unless you're just a really creepy guy or something lol, but assuming that you're a normal, decent person, I'd say you won't make her uncomfortable. She'll probably be happy that you finally talked to her =)

When there is a school dance, there was a time when all of the guys would stand on one side of the room, the girls stood together on the other side.

The middle area where the dancing supposed to take place was usually empty except for some couples or a few brave souls.

Why was the middle area empty?

Most on both sides were shy.

So, you are a shy guy, she is a shy girl.

Someone has to make the 1st move to break the ice.

Since she is a girl, she may be inclined to not make the first move...you being the guy, you need to do so.

You said it was odd to come up to her and say hello.

How is that odd?

How else are you going to break the ice unless you make the move.

Unless you got a better way to start a conversation with her, go ahead, approach and talk is the best way...unless you are too shy and that is too much of a task for you to get to know her.

If you want her to notice you, why bother with an indirect method?

How will she get to know you as a person if you go and find some way to hide or lessen your introduction to her?

No matter if they are shy or not, girls do like guys to have manly qualities including being confident in themselves.

If you claim you are shy and cannot be confident enough to speak with her, that is not a sign of being confident.

Either you are shy or you are confident, there is no middle ground or "buts' or exceptions to the rule.

I am confident in myself that I do not fear how a girl thinks of me if I was to approach her and introduce myself. She may be uncomfortable at first or she may not, however how I handle myself while I am chatting with her will make her feel more relaxed.

What words I say and how I present myself is how they know that I am not a stalker or weird.

If after I finish speaking with them, they do not find me appealing, that is fine, everyone is entitled to their own thoughts and judgement....many more females out there for me to chat with.

This is what confidence is.

No fear.

No shyness.

No stalking.

Just being myself.

Just learn that if you don't grow the guts to talk to this shy mysterious girl, some other guy will. We don't want that now.. do we? Confidence is key. Talk about weather if that's all you got, or ask casually if she's in school. Even if you know, still ask. Anything can open the door to a conversation, even how much you hate hitler.. but I doubt you should start of talking about the holocaust.

Try to find something you might possibly have in common with her. Maybe she has a school book and you could make a comment or ask a question about the subject? I am pretty shy, and I find is a lot easier when a guy asks me a question I can answer. Since you are both shy though, it needs to be something you can talk about and won't get a one worded response.