I like to see myself as pretty confident, but even for me situations where you're caught off-guard like you were can be a shock to the system. You stand there looking shocked for a bit and suddenly you're in hindsight mode and regretting not being totally cool about things. I like to imagine myself as someone I view as confident, like Ryan Reynolds or Ryan Gosling (I have a thing for Ryans, it seems), and I feel more confident. Lasts about as long as it takes me to walk past a window, but that can take a while. I watch how people I see as confident approach things, and I mimic that until I can do it on my own. Don't pretend to be them, just try to do what makes you feel confident. What makes you feel confident and how can you put that forward to her? For me, this is wearing my favourite hoody and being somewhere familiar. Things like that can make up the different between feeling completely unable to do something and barely able. Barely able is still able!
Try to remain honest. If she's interested in you, part of the evolution of a friendship/relationship is getting past the awkward stage, and getting to know each other. There's nothing shameful about being shy, it's pretty natural. She is a person, you are a person. If she's shy, suggesting things like going to a concert, the mall, movie or lunch/dinner (I dunno what you're into?) can be the easiest way around things - it give you a pretty basic script:
"Would you like to do this thing with me?"
"Yes"
Ask her what she's into, what she thinks about things. If you know something about what she likes, talk. If not, ask her about it. Keep the conversation moving by asking her things. This makes it slightly less stagnant and also lets you into her brain a bit, you get to know each other.
"I hear you like this band."
"Yeah, they're great."
"I haven't heard much from them, but they seem really good - what are your favourite songs?"
Girls love it when you're into what they like, but don't fake it. Try to instead find a middle ground. Ask her questions. If she asks why you're asking so many questions be honest and tell her you want to get to know her. Don't dance around things like that. If she likes you, she'll be totally okay with you being interested in her.
The hardest part around talking to someone you like (or even just someone you don't know) is actually doing it. It's scary for some people, and it takes a lot of work to get over that. I still get scared talking to new people, and they're not even people I want to be friends with or date. I fake confidence until I am confident, but that takes practice.
You might know what to say but when you actually get to the moment it's pretty nerve throttling. Confidence is something you have to build, so practice in your head. You've talked to her a bit already and so use that as an example. She's shy, so that can make things harder on you - You're shy too, and so help yourself by knowing what you're going in there to talk to/ask her about. How would you react to her coming to YOU to talk? What would you say?
Be yourself, if she likes you that's usually enough. The awkwardness will pass. It's really hard and it sucks, but you've got to work at it. That's where friendship starts, usually. Right at the bottom.
And if you can imagine Ryan Reynolds/Gosling telling you all this, that'd be great, thanks. Good luck dude, relax!