a. In the bunny
b. In the gravitational field of the earth
c. In the gravitational field of the bunny
d. In the gravitational field of the system
The conversation became somewhat sematical (is that a word). One could argue that the bunny stores the energy in the earth's gravitational field. Or could they? If a single mass occupies an otherwise massless universe does it have a gravitational field? Likewise if a positive point charge occupies an otherwise chargeless universe does it have an electric field?
Electric field lines help us to conceptualize the electric field and they are defined to begin on a positive charge and end on a negative charge. If a lone positive charge were to have electric field lines emanating from it they would be spherically symmetric. However where are the lines going? They either go somewhere or they don't. If they go somewhere then the somewhere is negative but we just said that there is no other charges in the universe. Hmmm then I guess they go nowhere and they don't come from the charge and therefore we don't even know the charge is positive.
In a like manner if there are no other masses in this otherwise massless universe (except for one point mass) then there must not be any gravitational fields associated with the mass and therefore there would be no mass associated with this lone "mass". Hmmmm. So where does General Relativity come in here? There would still have to be some effect of the lone object's mass on space-time. So is there still a gravitational field here? Would there still be an electric field for the lone "charge"? Too many questions . . . too few answers.