I could really relate to your post. Do not worry, your experience here with your best friend is not uncommon (not that that makes it any easier for you, but just know it's not unusual), I had a similar experience with my best friend in high school (not sure of your age, but highschool/start of uni was when it happened with us).
It's a tricky situation, especially as your friend has alluded to being interested in exploring things away from purely heterosexual when she said "am I even straight?" (even if she was joking). But I would be wary of instigating anything with her, or revealing your feelings for her, because losing her friendship is a risk you don't want to take.
That being said, there could come a time where things just happen between you ... it could evolve into something more ...
I can't advise you on what to do, but I can tell you what happened with me, and that is that something more did evolve between us, but it didn't go anywhere, and it was never meant to be. Many, many years later, here we are, still great friends, her with a husband and 4 kids and me with my beautiful (female) partner.
I think it's common for confusing feelings between very, very close friends, even between "totally" straight friends, but you have the added element of identifying as bisexual, so, I understand your pain!
Sorry I haven't been much help, but I'm here to chat with further about it if you would like, any time.