Were you using the correct term, then?
As a bisexual, bigendered person in a relationship with a bisexual cisgendered person, and a sister who is pansexual…
I understand the definitions as such:
Bisexual: Desiring both common genders for partners.
Pansexual: Desiring a partner regardless of gender.
As such, bisexual is inherently Poly (either looking for one-off flings to meet that instinctive need or seeking a lifelong committed triad or quad relationship as my partner and I are).
If you dread the question, could you be pansexual instead of bisexual?