The key approach to successfully asking a shy girl out will be the "Come To Her Comfort Zone" technique.
Why Do They Always Say No?
When I first met the guy I am currently dating, I was very shy. He indirectly made it clear that he liked me, even though I rejected each of his offers to hang out in the beginning. He even went on to say that it didn't need to be a date, but more of a hang out. Still didn't work.
The reason I rejected his offers was because I did not know him well enough. I didn't feel comfortable enough around him. I needed to to feel more at ease with him before hanging out just the two of us. A shy girl needs to know what type of character the guy is before she can feel free to be herself with him so that she can know how much of herself to show without feeling embarrassed.
The Secret Technique
Most shy girls secretly know exactly what they need from a guy, so that they can overcome their nerves and go on a date with him. In fact, many of these girls are disappointed that most guys don't care to know a girl unless she is naturally outgoing. They often day dream of the day when a guy will finally notice and take the time to know them.
Here is how the technique works.
With most shy girls before you ask her out, it's always best to get to know her in an environment that she is already comfortable in. For example, where do you typically see her? At school? Work? group meetings? etc... If you know her from school, why not ask if you could join her and her friends during lunch? If you are getting to know her someplace she already feels at home, she is most likely to open up to you and be herself. It is the best way to get to know a shy girl.
Me and my boyfriend met at church. Church was one of my comfort zones because I knew the environment and I knew the people well. The first few times we hung out was at youth group. Once we started knowing each other better, the first step he took to gradually bring me away from my comfort zone was the following:
"The guys who end up dating the shy girls are the ones who are persistent and patient at pursuing them."
Our whole church had had planned to go see a movie at the theater, and he had asked me to sit beside him during the event. When I got to the show, he followed through with what he said, and reserved a seat for me beside him which prevented me from bailing on him, even though I was super nervous. See how I was in a comfortable environment with people I knew, and he simply asked me to sit beside him. Because he followed through by reserving me a seat and calling me over, I did! It might not seem like much, and I was very nervous the whole time, but is was so exciting to me and I loved it!
After that night, we started seeing each other outside of the church. Him and his family came to my house for supper and then we saw the Christmas parade together. Soon enough, we were going on real dates just the two of us!
To The Point
When it all comes down to it, not many guys actually take the time to get to know the shy girls. The fact that my boyfriend was so patient and persistent with me (unlike most guys) is what sparked my interest towards him in the first place. The guys who end up dating the shy girls are the ones who are persistent and patient at pursuing them, who know how to properly apply the "Come To Her Comfort Zone" technique.
Good luck with that special girl!