The implication of the pet rabbit as I understand it (and this is just my opinion) is that, as a child, Bibi was negligent with a thing she loved. She misunderstood what it meant to love something, and as she says, "I thought it'd like whatever I gave it." One can even question if she really did love the rabbit at that point, or if she loved that the rabbit loved her. Whatever the case, she most certainly seems to have felt responsible for it (and its subsequent death). Now, she's flipped to the far extreme, which is an overbearing control. She's influenced aspects of Amy's life to bring her closer to her (Bibi) and the idea seems to be that this time she's not going to let go of Amy, because she wants Amy to keep loving her. There are certainly suggestions of a more reciprocated love that Bibi is feeling, but given her character, I can't help but wonder.