no concept of healthy relationship/dating

Relationship/dating at a fundamental level is two people getting their needs met. A dysfunctional relationship is when one or both of them has dysfunctional needs (eg: a person who likes fixing things so they date someone whose life is a mess). A healthy relationship is people with healthy needs.

Your needs are something like: you want sex, intimacy, to experience dating. This is healthy. Whether you and this girl are compatible is an unknown at this point. You owe it to yourself to pursue her and find out. She should grateful that you have taken the initiative, it gives her an opportunity to have her needs met. If it doesn't work for one of you than you, or she, should walk away.

She is really shy and new to the dating scene

So you do her a favor by being strong and taking initiative. Escalate fast regardless. If she ever seems anxious be the strong man she needs and reassure her that you will protect her, her well being is important to you.

Surrounded by fucking drama and I'm afraid I'll become a part of it

If you're ever ridiculed for asking a girl out then, well, what a ridiculous thing to be made fun of for. Don't be afraid to live by your values.

I'm a shitty loner with no method of transportation

Sounds like you have more to work on than this girl.

Her sister is also with us during rehearsals

I wouldn't waste any energy worrying about her sister who I doubt cares about this one way or the other.

I don't want all communication between us to cease because I really like this girl.

Here's the horrible sad truth. If you don't present yourself as a sexual partner now it becomes almost impossible later. Girls are different than guys. A guy sees a hot girl and he wants to fuck her then and forever pretty much no matter what. A girl sees a guy and she's usually fairly neutral. Then she slowly groups him into "potential lover" and "just friend" groups where her whole perception of the guy evolves differently. Once you're a friend you might as well be her brother - she'll never want to fuck you.

You have to pursue her sexually NOW. You need to present yourself as someone sexual to her, someone she could date, someone she could fuck. Go watch a James Bond movie and watch how he interacts with women. Sex is never off the table, he's never just a friend. And every girl swoons over him. If James Bond tried to get buddy buddy with a girl because she wasn't ready to date I promise you she would never want to fuck him ever, he'd be "just a friend - like a brother, ewwww". I know he's fictional but there's a lot of truth behind why he's a lady's man.

Gimme some advice, doc.

Here's my advice:

• pursue this girl. Get her number. Hang out with her. Try to be relaxed about it all, it's just two people hanging out, it doesn't have to be a big deal. But you're not her buddy - remember, you are a sexual man.
• read, No More Mr. Nice Guy by Robert Glover, a great book about being a man and dealing with women. You're worried about everyone but yourself. I think this book, though it might seem a bit wacky at first, will help you live by your values. (It's also on audiobook).

Do the two above starting now. Don't use #2 as an excuse to avoid #1. You owe it to yourself (and you do this girl favor) by taking initiative and escalating the relationship.