Please help! How should I approach another woman?

Alright, so there's this girl in my course that's really awesome (at least, I think that she is). She is extremely physically attractive, and she's an amazing artist. I definitely get butterflies when seeing her all the time. I've only had 3 classes at this pre-college thing so far, so I don't really know her very well. Actually... I don't really know anything about her. But I WANT to get to know her! I can tell we have some things in common because we both like art, and The Beatles (I saw her pin on her bag, lol.) I'm the type of person who is really self-confident 90% of the time, but when I'm interested in someone I kind of crawl into a shell, sometimes. I really want to ask her for her number so I can spark up a proper conversation with her, and I'm not exactly sure how to go about that since I'm totally head over heels for this girl! I tried to do little things like make small talk, tell her she's a good artist, etc... It seems to work well because she's really friendly to me. She's even offered to let me use her bin for art supplies. I'm not sure if she's trying to be genuinely nice, or if she's picking up on my flirting. Probably not because a lot of us know what I mean when you're trying to flirt with someone and it seems as if they're REALLY not getting the hint, haha. Of course I want to know the magic question- what's her sexual orientation?! I can't tell if I'm being flirty enough. I don't think "Hey, your drawing was so great this week, it was definitely my favourite!" warrants well enough as what I want to come across as- which is "HEY YOU'RE BEAUTIFUL!!! We should go out on a date sometime!":icon_wink
Does anybody have any advice for me with this? Is there something I can maybe do that would make it more obvious that I like her without looking like a damn idiot? Thanks a bunch in advance!