How to ask a girl to hang out?

please read this part, its all important. I'm 16 (boy). there's this girl I like and she's kinda popular and is an outspoken person that's pretty artsy. were both in science together and basically we started talking after we had a study group with one of my best friends (girl). my best friend is best friends with the girl I like. anyways I just were decent friends we talk pretty often but were still getting to know each other and the school year is ending and usually all the times that I have hung out with her we were either always trying study. now that the school years ending I don't wanna end up not talking to her, so I want to be able to hang out with her but were not close enough yet for me to ask her out for like a date. so how can I ask her to hang out casually like without sounding creepy? what kind of things can I ask her to do with me? also although I'm 16 I can't drive yet and my parents are kinda strict and don't like me hanging out with girls alone or people they don't know so I need to think of an excuse for a ride. things we share in common is that were very liberal so we share a lot of views and morals and also we both have similar music taste if that helps. remember I want to ask her to hang out as friends for now. I really wanna be able to spend time with this girl and get closer to her so that I might actually have a chance with her!