Should i ask her out?

(im a freshman in college) there is a girl in my econ class and i think she's really cute, and she was in my english class fall quarter too, but i didnt ask her out then cause i was dating someone. but now that that ***** is gone, and i feel ready to get back into the game i want to ask her out but neither of us have talked to each other at ALL, and the year is almost over. i only have 2 classes left before we're off for summer vacation. this friday and next monday for our final. im transferring to main campus for next year too. could it be fate that we were in the same classes again? im not the most outgoing guy either. ive only had one girlfriend in my entire life (i know pathetic) im pretty shy and not the kind of guy to just walk up to someone and ask them out. so should i ask her out and how should i? ill answer any questions too.