The thing about bisexuality is that it doesn't matter which genitals you get.
So many pseudo-bisexual-populars seem to think of the bisexual orientation as a golden ticket to have a complete set of all genital makes and models at all times.
When your attractions to people are primarily based on internal qualities, charm, warmth, openness, honesty, sense of humour, intelligence, endeavour, spirit, you quickly realise that gender doesn't matter. Bisexuality to me is when you can fall in love with someone based on these qualities and without regard for which style of genital apparatus they are attached to.
Not to assume that genital apparatus can adequately describe someone's gender. Gender is a continuum, not a binary digit. A person's gender identity can differ from his or her anatomical gender.
To suppose your boyfriend won't mind sharing you, just because you're a 'bisexual', is just sad and ignorant. Having a bisexual orientation is not a license to cheat. It is an opportunity to love someone deeper and beyond their gender. Something precious. Giving it to more than one person at the same time is polyamory, not bisexuality. Perhaps you should ask your partner if he will share you, because you're polyamorous? See how far you get with that one.
Is it any wonder that bisexuals struggle so hard even for a title?