The Fermi Bubbles are enigmatic gamma-ray features of the Galactic bulge. Both putative activity (within $sim$ few $times$ Myr) connected to the Galactic center super-massive black hole and, alternatively, nuclear star formation have been claimed as the energising source of the Bubbles. Likewise, both inverse-Compton emission by non-thermal electrons (`leptonic models) and collisions between non-thermal protons and gas (`hadronic models) have been advanced as the process supplying the Bubbles gamma -ray emission. An issue for any steady state hadronic model is that the very low density of the Bubbles plasma seems to require that they accumulate protons over a multi-Gyr timescale, much longer than other natural timescales occurring in the problem. Here we present a hadronic model where the timescale for generating the Bubbles hadronic gamma -ray emission is $sim$ few $times 10^8$ years. Our model invokes collapse of the Bubbles thermally-unstable plasma, leading to an accumulation of cosmic rays and magnetic field into localised, warm ($sim 10^4$ K), and likely filamentary condensations of higher density gas. Under the condition that these filaments are supported by non-thermal pressure, we can predict the hadronic emission from the Bubbles to be $L_gamma simeq 2 times 10^{37}$ erg/s $ dot{M}_mathrm{in}/(0.1 M_{Sun}/$ year $) T_mathrm{FB}^2/(3.5 times 10^7 K) ^2 M_{fil}/M_{pls}$ ; precisely their observed luminosity (normalizing to the star-formation-driven mass flux into the Bubbles and their measured plasma temperature and adopting the further result that the mass in the filaments, $M_{fil}$ is approximately equal to that of the Bubbles plasma, $M_{pls}$).
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