Seems like you have a few options:Here's the thing. I've had this happen before and I know that if someone really likes you there will be more confirmation in terms of talking frequently about each other's interests. We do that in some ways actually... from previous experience, it will turn into dating whether you asked her out or not.
We live closeby and she visits all the time, and works for a relative, and I have a connection with that relative and that relative hates when people date their co-workers.
I havent asked her because I don't want it to put me in a bad situation with that coworker because he's like a co-supervisor.
So over time I've noticed and liked her back because of the chemistry, but initially there was a distance and no view or attitude toward liking her on that level
Ignore her attentions because you cherish the relationship with your relative/co-supervisor more // the power dynamic is a bit complex.
Entertain her attentions and date her even though your co-supervisor might not like it.
One of you quits, and you date.
Only you would be able to know if you're ready for the consequences of these decisions (good and bad)!