  We show that the Virasoro conjecture in Gromov--Witten theory holds for the
the total space of a toric bundle $E \to B$ if and only if it holds for the
base $B$. The main steps are: (i) we establish a localization formula that
expresses Gromov--Witten invariants of $E$, equivariant with respect to the
fiberwise torus action, in terms of genus-zero invariants of the toric fiber
and all-genus invariants of $B$; and (ii) we pass to the non-equivariant limit
in this formula, using Brown's mirror theorem for toric bundles.
