What difference. What is the difference if she were heterosexual? Monogamy isn't special to heterosexuals and trust is trust. How can she be sure you won't cheat on her with another woman? Maybe if you can answer that question, you can apply it to her. Keep the relationship happy, caring and loving to reduce any reason for cheating.
Trust. All relatioships are a matter of trust. Your situation is unique but if you enter a relationship with the knowledge that she is bisexual then you have to discuss exclusivity in your relationship just as two heterosexual people would. If she agrees with that then you have to trust her if she disagrees then you have to re-evaluate your expectations.