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Should I ask this girl out?

Ok so there's this girl and I think she likes me. She always looks at me during class and whenever I look back she quickly looks away. Whenever I talk to to her she smiles a lot and looks kinda shy. She also giggles a lot. Whenever I ask a question to someone in front of her she answers it really fast (before the person I asked the question to). The other day, she ask me to pick her eraser up because it fell on the floor (I think she may have dropped it on purpose, because in the circumstances it was almost impossible for the eraser to fall by itself) she also seems to always or everywhere I go in the school. Should I ask her out? If so what should I do? I'm 16 and I never had a girlfriend, because I'm shy and now I'm tired to be shy XD
Should I ask this girl out?
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