Herringbone-grooved journal bearings (HGJBs) for high-speed turbo-machinery are often supported on O-rings due to their favorable stiffness and damping characteristics for stability and alignment reasons. They yield limited lifetime at high temperatures, insufficient assembly repeatability, and dynamic characteristics that are difficult to measure and to tune, however. In order to overcome these shortcomings, a parametric model has been developed with the aim to design a flexible membrane bushing support that offers tunable tilting and radial stiffness and that can be coupled to various concepts to provide suitable damping levels to support a gas-lubricated bearing bushing. Three damping concepts have been investigated that offer independent tuning of the support damping coefficient in combination with the novel flexible bearing bushing support. The new flexible membrane support was manufactured and its stiffness in radial and tilting directions was measured before it was successfully implemented in a prototype. Test results obtained from the new prototype with membrane support show a significant improvement in bushing alignment quality compared to O-rings as well as stable operation up to the design rotor speed of 250 krpm.