  We study the formation of superradiant bound states for massive scalar fields
in five-dimensional rotating black string geometries with a non-vanishing
Kaluza-Klein momentum along the compact direction. Even though all Kaluza-Klein
modes may form bound states in this geometry, in realistic extra-dimensional
models and astrophysical black holes only the zero-mode is sufficiently light
for superradiant instabilities to develop, provided the field has a small but
non-vanishing mass, as for example for axion-like particles. We use analytical
and numerical methods to show that, although the Kaluza-Klein momentum
decreases the upper bound on the field mass for an instability to develop, it
may enhance its maximum growth rate by more than 50%, thus boosting the black
hole bomb mechanism. We discuss the possible observational consequences of this
result and its potential as an astrophysical probe of non-trivial
extra-dimensional compactifications.
