In the second of two papers on the peculiar interacting transient AT 2016jbu, we present the bolometric lightcurve, identification and analysis of the progenitor candidate, as well as preliminary modelling to help elucidate the nature of this event. We identify the progenitor candidate for AT 2016jbu in quiescence, and find it to be consistent with a $sim$20 M$_{odot}$ yellow hypergiant surrounded by a dusty circumstellar shell. We see evidence for significant photometric variability in the progenitor, as well as strong H$alpha$ emission consistent with pre-existing circumstellar material. The age of the resolved stellar population surrounding AT 2016jbu, as well as integral-field unit spectra of the region support a progenitor age of >16 Myr, again consistent with a progenitor mass of $sim$20 M$_{odot}$. Through a joint analysis of the velocity evolution of AT 2016jbu, and the photospheric radius inferred from the bolometric lightcurve, we find that the transient is consistent with two successive outbursts or explosions. The first outburst ejected a shell of material with velocity 650 km $s^{-1}$, while the second more energetic event ejected material at 4500 km $s^{-1}$. Whether the latter is the core-collapse of the progenitor remains uncertain, as the required ejecta mass is relatively low (few tenths of M$_{odot}$). We also place a restrictive upper limit on the ejected $^{56}$Ni mass of <0.016 M$_{odot}$. Using the BPASS code, we explore a wide range of possible progenitor systems, and find that the majority of these are in binaries, some of which are undergoing mass transfer or common envelope evolution immediately prior to explosion. Finally, we use the SNEC code to demonstrate that the low-energy explosion of some of these systems together with sufficient CSM can reproduce the overall morphology of the lightcurve of AT 2016jbu.
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