I wouldn't ask her out via email.
In fact, personally, if I was in your boat, would never "ask her out."
You only ask people out if it is the only way you can gain access to them to seduce them.
You have access. Use it.
I seriously doubt you don't have any other opportunity to talk to her. You are just not being creative enough.
Every second in class you can seduce her. Whatever it was that you planning on doing on this date to make her wanna **** you you can do it in class.
Personally I would wear cool clothes, have a nice smell, flirt with the other girls, be loud and crazy with guys, skip class every now and then, be the class clown, make sure I have great body language and voice tone, bust on her or ignore her most of the time but occasionally give her some serious EC...
If you generate attration in her she will put herself in a position where you can approach.
As for the email, I'd only use lighthearted topics to keep her thinking about you and ONLY after I have began to generate attraction in person.
save the DJ stuff for face to face.