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I don't see any difference between dating a straight person or a bi person. If it is a fear of cheating, is not the gender of the third party irrelevant. Will she go full lesbian, same issue as will a straight girl go off me.
On the plus side if she is comfortable enough to accept her bi-sexuality chances are she has good self confidence and be open minded, qualities I admire a lot in women. Also if she has dated women she may be able to give relationship a fresh novel approach.