first of all breath you seem to be working yourself up over this.
Don't worry too much about seeming shy, it's better than being smarmy and fake. Try to chat with her a couple of times before you ask her out, to find out what she's interested in.
Find some conversation starters by watching TV or reading newspapers. Ask her some questions like what music she's interested in but don't bombard her with them.
Think of ideas for your first date before you ask her out. Don't plan anything too complicated. The purpose of the first date is to spend time together and focus on each other.
Ask her out when she's not busy and when there's no one else around. Remember the more attention you're paying her, the less you'll focus on your own nervousness. Take a few deep breaths. Oxygen will help your thinking and keep you calm. Finally, gather all your courage and confidence and go for it.