Hi Luigi, welcome!
Hunter is right on! She initiates conversation with you - she likes you, at least at some level.
Young guys have a really tough time with this (to be honest I did too when I was younger and less confident - dude, just saying that makes me feel old, lol)... and often times they will miss an opportunity to have a relationship with a great girl because they get stuck in self doubt and indecision - and by the time they look up the girl's gone.
Definitely, go for it. Just remember there's no "right" and "wrong" approach or things to say, etc. So I can't tell you the exact things to say to her or the exact things to wait for her to say - it just doesn't work like that.
One day, one moment she may be attracted to you, but if you wait 3 days, the situation may be completely changed. That's life... opportunity likes speed. It comes to you and you either seize it or watch it walk away.
But what if she's not interested after all?
So what. Seriously. If you find out that she isn't interested in you that way - it's ok! But unless you try you'll never know and you're guaranteed to be alone. Right?
And get this: the most successful people in the world have innumerable strikeouts behind them - but they kept at it, kept improving their game / strategy / themselves, and kept the faith. Always keep the faith.
Honestly this is usually a confidence thing. Read
this thread on how to build up your confidence, that is crucial to being attractive to women. Absolutely crucial
Oh, and also check out this
great thread on how to know you're making the right decision - and what to do if you're afraid you may make a wrong decision.
Also check out these two similar discussions on how to tell if she likes you:
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Does she like me?
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I really like this girl but dont know if she likes me or how to ask her out or anything! please help
Come back and let us know how it goes!