We prove that single G-weighted \(\mathfrak {b}\) -Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights G. Consequently, the \(\mathfrak {b}\) -Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of \(\mathfrak {b}\) -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.
