Does she like me as friend or maybe boyfriend??

Ok, heres the situation. You see there is this girl I met at uni during a tutorial session about 2 months back. During that session, we had a good conversation ~ and she left me her email after that class. I asked her for a lunch the week after, and we spent about 3 hours together that lunch (coffee, walk, talk etc.).. from there its been two months so far and we meet about 2-3 times a week, each time around 3-5 hours.

She's always alone with me (just us 2), been to the movies, ice skating and bowling together during these 2 months also~ (we often pay for one another sometimes, she pays for lunch, i pay for movie, that type of thing)

But you see, I really dont know whether I should pop the question bout her being my girlfriend etc.. I havent held hands with her either~ We both are quite shy, and I give her heaps of space when we not meeting up (only sms her etc)
So does she like me as a friend or boyfriend.. and should I pop the question anytime soon or wait it out a bit longer

it seems to me she really likes you bud! .. yeh go aheah and ask her. if she didnt like you. TRUST ME! she wouldnt even go out with you if she didnt. i bet she is praying and dying for you to pop the question, .. i hope things work out. ps. i think shyness is cute in a guy! .. good luck