  We find a family of complete non-linear Kaluza-Kein reduction ansatze from
type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic
sector. The reduction is over a sphere $S^2$ and a Riemann surface $\Sigma$,
and depends on a pair of arbitrary locally holomorphic functions
$\mathcal{A}_{\pm}$ on $\Sigma$. This family of reductions is inspired by the
recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB
supergravity that depend on these same functions $\mathcal{A}_{\pm}$.
