Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requirements. However, they are more complex to operate and exhibit nonlinear behaviors. This paper presents a parametric hyper reduced order model (h-ROM) of a gas bearings supported rotor enabling to speed up the computations up to a factor 100 while preserving satisfactory accuracy. A Galerkin projection setting is employed to reduce the dimension of the governing equations and the nonlinear terms are efficiently tackled with a sparse sampling technique. The performances of the h-ROM are compared to a high fidelity model both in terms of accuracy and computation time, demonstrating the potential for future anomaly detection applications.