Is it bad form to ask someone to be my advisor over email? The faculty, of course, will not first hear from me over email - we have maintained semi-regular research-related meetings over the semester. I have not yet asked her to be my advisor, but now since the academic year has ended, I want to make this an official advisor-advisee relationship. I'm wondering if it would be bad form to just ask the question directly over email, as she doesn't seem to be around the department anymore. I should add that I am already a PHD student in the department, and funding is provided by the department, so I am not really asking for money either.
I would first send her an email asking when she might next be around campus and able to meet.  If she responds that she's traveling (which is entirely possible now that the academic year is over), I think you can send a polite follow up asking her to be your official advisor.