I think that the main question here is: do you want her to break with BF for you? If you didn't want her to be with you then probably Tumper is right.
Due to my lack of experience with taken girls I might not be in the position of confirming this, but I can tell you what happened to me in similar situation when I went for option two.
I wanted a girl to be with me, I f-closed, she broke with BF telling him that she cheated on him hence they cannot be together anymore. She also had doubts about him, sleeping with me probably was just a good excuse for her to leave him. Guy got mad, threatened me – he was taller than me by two heads at least, easily could beat me up to pulp but fortunatelly she told him I was into some judo stuff so he also wrote that he is only “considering beating me up” (what he didn’t know was that I really sucked at judo).
Anyway... We moved together and after ten months she left me for a pretentious fire poi street performer.
Hope that my story is any help
