quick, I think what Ann pointed out is the most important thing in this situation. "Does she have any supervisory role in your research..." In my opinion, if she has nothing to do with your research, what you do is nobody else's business. It sounds like early days, so it's normal to have that electricity, and it's not a bad thing. It might be a fling, or it might be a bigger thing. You can work this out in time. But if she is part of your research team, then it's a different situation, so your supervisor would have every right to stick his nose in it.