Yes I would. If she wants to date me and wants to be monogamous, while it is true that she may be bi, it would seem that her desire to be both with me and monogamous speaks for itself. This isn't to suggest that her bi-sexuality goes away while dating me, just that the person in question has chosen me. Now if she wants to be with me and then exercise her bisexuality and have a girl friend as well, then this isn't monogamy so it sort of rules out that sort of a relationship. Lastly if she wants to be with me and a girlfriend and we are all together, this can be something that might work, but it is important to note that all parties have to know what is going on (no secrets) and all parties have to be compatible both personality wise and sexually. If all of these things can line up than, yes I would be willing to be in that sort of a relationship. However I know that it will require a great deal of work really for everybody concerned.
Where the relationship was one of monogamy or polyamory, I would be willing to date her. I don't understand why some guys would refuse a girl because they were somehow threatened that she liked other women.
Personally, I would be slightly disappointed if she was never willing to bring in a third party, either just for a night of fun, or as a full third person to share our relationship with, but keeping your partner happy and content is more important that fulfilling fantasy, so if monogamy is what she wants, strict monogamy is what we'll have.