I wouldn’t worry so much at this point whether or not your daughter is truly bisexual. Adolescence is the time in life in which you develop your identity, which by it’s very nature requires some experimentation, both in theory and through behavior.
I would be more concerned about the Borderline Personality Disorder traits that you mentioned, the lying and attention-seeking behaviors. However, again, this may just be part of her trying to figure out who she is and test limits. If the patterns continue and she begins using social media to hurt others, then it’s obviously a more serious issue.
It sounds like you are good parents who set appropriate boundaries with your teen. Have faith that these parenting skills will pay off and she will emerge from this stage of development with a strong sense of who she is in the world, but be willing to let her test her wings in the meantime. In the end, if she really does identify as bisexual, I hope that you can accept this and love your daughter unconditionally.
All the best,
Dr. Holly Counts