Dating in grad school
I invited her along when I hung out with other students in my class.
And eventually, I asked if she wanted to go on a date. One last thing you should think about, Mahnanymous, as you get to know your crush: dating someone/breaking up with someone in the same academic field has major pros/cons.
Obviously, as others have said, it would be unethical to violate the expectations set up in your school's policies (unless the policies themselves were unethical, such as Bob Jones University's old ban on interracial dating).
Dating someone that’s in your same academic field can be fantastic. Good luck talking to Crushy Mc Cuteface, and best of luck in your grad program!
There’s something amazing about dating someone who just GETS IT: who knows the words you’re using, who can intelligently pick apart theory, who can act as a sounding board for your ideas. That being said, if you break up with someone in your grad program, you’ll still see them regularly. And well into your academic career—at the conferences every year, at the symposia you organized, at the women in science workshop you’re going to.
(Grad school is broad, after all...) If you study social psychology and she studies sociology of groups, say, you might have too much overlap to ethically date: she might have to curtail her academic interests to avoid taking your classes.
(That said, it would be problematic on the other hand if you two developed an academic relationship with an unrevealed desire for a romantic relationship still lurking.) Also consider what would happen if you dated but broke up acrimoniously.