I don't think this is a fair situation to you. Her sexual orientation is not an excuse to go outside of a relationship. Bisexual people can very well manage to have a monogamous relationship with either gender, it's about the commitment, not the desire.

The question is not whether she's bisexual and wants to go explore, but that she wants to open the relationship and go be with other people.

You need to discuss with yourself whether you are willing to be hurt like that just so she can have fun, and then have a discussion with her about how it hurts you regardless of what gender she wants to go with. She will either choose you and stop what she's doing, or you walk away for your mental health.

If you love your partner and are committed to them and claim 'you don't want to lose them', then you don't go out of the relationship to seek for someone else, male or female