Just ask her if you two could catch-up. CATCH-UP! Juuuust the 2 of you
then when you're catchin-up, ask her out. I know it sounds easy but its actually really hard, but just don't let the "catch-up" stay like that. Otherwise its friendzone, and for a shy guy like you, friendzone = death. :D
so just catch-up, ask her out, and hopefully she'll be your gf.