Coping with synchrotron radiation (SR) that originated at superconducting bending magnets is one of the major challenges in the design of the vacuum beam pipes of hadron colliders. In the case of the Future Circular hadron Collider (FCC-hh), similarly as for the LHC, a beam screen, operating at higher temperatures than the cold mass, has been designed in order to preserve the superconducting magnet cold bores from direct synchrotron irradiation. The quality of the beam screen vacuum can be severely compromised by the absorption of SR into its walls, enhancing the risk for numerous beam detrimental effects to arise. In order to experimentally study such effects and develop strategies for their minimization, a beam screen test bench experiment (BESTEX) has been conceived and installed in the Karlsruhe Research Accelerator storage ring at the Karlsruhe Institute for Technology. The BESTEX has been designed to explore photon stimulated desorption, photon reflectivity, photon heat loads, and photoelectron generation originated on beam screen prototypes under irradiation of the FCC-hh-like SR spectrum. A detailed description of the BESTEX, its commissioning, and its functionality is hereby presented.