Some people assume that bisexual people are automatically non-monogamous.
But this is not the case. For a bi person in a monogamous relationship, calling themselves bisexual says something about their potential to be with either a woman or a man. It doesn't mean they need both right now . It may mean that supposing they split up with their current partner, they could imagine being with either a woman or a man next. It may mean that they never imagine splitting up with their current partner, but they still call themselves bi to acknowledge their attractions to both women and men.