  Draining vortices with a free surface are frequently employed as rotating
black hole simulators, both in theory and experiments. However, most
theoretical work is restricted to the idealised regime, where wave dispersion
and dissipation are neglected. We investigate the role of these effects on the
analogue black hole bomb, an instability resulting from rotational superradiant
amplification in confined systems. We reveal that the dispersion of deep water
capillary-gravity waves significantly modifies the unstable mode
eigenfrequencies, whereas viscosity only affects those with high frequencies.
Furthermore, if the circulation is less than an order 1 multiple of the drain
rate, superradiance does not occur and the vortex is stable. The instability is
maximised in small systems with high flow velocities, provided there is
sufficient space between the vortex and the outer boundary for the first
excited state to lie inside the superradiant bandwidth. Implications for
experiments on analogue black holes and free surface vortices are discussed.
