b -Hurwitz numbers from refined topological recursion

We prove that single G-weighted $b$ -Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights G. Consequently, the $b$ -Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of $b$ -monotone Hurwitz numbers, and the enumeration of maps and bipartite maps (with internal faces) on non-oriented surfaces. As an application, we prove that the correlators of the Gaussian, Jacobi and Laguerre $\beta$ -ensembles are computed by refined topological recursion.