First: Being bisexual doesn't equal being poly. There are plenty of monogamous bisexual people out there. Your problem is that she wants an open relationship, not that she is bi.
Second: I would be very leery of any partner that wants something but sets restrictions based upon jealousy. I find it funny when people say "I want to sleep with other girls and I wouldn't be jealous if you slept with a guy, but I will be jealous if you slept with a girl" or vice versa. This is one reason why I don't fit in well with he swinger community because although most of the couples claim to be open, there is a hell of a lot of jealousy simmering underneath a whole lotta denial.