Forward Proton Detectors at the CERN LHC aim to study soft and hard diffractive events from high-energy proton-proton collisions. Time-of-Flight systems at the LHC are used to reduce the background from multiple proton-proton collisions. In this presentation, we describe technical details of a fast Cherenkov model of photon generation and transport through quartz bar-shaped Cherenkov radiators of a ToF detector. The fast simulation uses Python programming language and Numba - high performance compiler. The calculation is about 200 times faster than a typical Geant4 simulation and provides comparable results concerning path length and time-of-arrival distributions of photons at the photon detector. Moreover, the fast simulation allows easy computation of the time resolution of the different Cherenkov bars of such a time-of-flight detector.