If your partner is bi already, then they pretty much by definition are already sleeping with you, as well as someone not your gender.
In the general public, most people are monogamous, at least outwardly. So if they are bi, and coupled up with a man, they are not likely to be "sleeping with" a woman at all. They are mono, so they only love and have sex with one other person.
But if your partner is bi and polyamorous, or polysexual, and dating you, a man, they might be dating a woman, or women,
or other men.
If they are pansexual and poly, they might be dating you, and a woman, and a another man, and a transperson, and a non-binary person. It all depends on if they have the opportunity and luck to have met people they are attracted to.
Just because you feel bisexual doesn't mean you
have to date two people, one of each gender.
Just because you are a heterosexual man doesn't mean you
have to date multiple women. If you are a committed monogamist, you'd only date one woman at any one time (if you're lucky to find a good one). If you are a poly hetero man, you might date no women, one woman, or multiple women.
Hopefully someone else with more experience will also advise.
To sum up, being bisexual does not automatically mean "I
must date one person of each (binary) gender." It just means, "I am attracted to both genders." Being attracted to people is a feeling. You can't help feelings. Actually dating and/or having sex with more than one person of any gender you're attracted to is a
choice, and choices are under your control.