$$\mathfrak {b}$$-Hurwitz numbers from refined topological recursion

We prove that single <i>G</i>-weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi></mml:math> -Hurwitz numbers with internal faces are computed by refined topological recursion on a rational spectral curve, for certain rational weights <i>G</i>. Consequently, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi></mml:math> -Hurwitz generating function analytically continues to a rational curve. In particular, our results cover the cases of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi></mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> -ensembles are computed by refined topological recursion.