We investigated the influence of the photobleaching (PB) effect on the dosimetry performances of a phosphosilicate single-mode optical fiber (core diameter of 6.6 µm) operated at 638 nm, within the framework of the LUMINA project. Different irradiation tests were performed under ~40 keV mean energy fluence X-rays at a 530 µ Gy(SiO2)/s dose rate to measure in situ the radiation-induced attenuation (RIA) growth and decay kinetics while injecting a 638 nm laser diode source with powers varying from 500 nW to 1 mW. For injected continuous power values under 1 µW, we did not measure any relevant influence of the photobleaching effect on the fiber radiation sensitivity coefficient of ~140 dB km-1 Gy-1 up to ~30 Gy. Above 1 µW, the fiber radiation sensitivity is significantly reduced due to the PB associated with the signal and can decrease to ~80 dB km-1 Gy-1 at 1 mW, strongly affecting the capability of this fiber to serve as a dosimeter-sensitive element. Higher power values up to 50 µW can still be used by properly choosing a pulsed regime with periodic injection cycles to reduce the PB efficiency and maintain the dosimetry properties. Basing on the acquired data, a simple model of the photobleaching effect on a coil of the investigated fiber is proposed in order to estimate its sensitivity coefficient evolution as a function of the cumulated dose and its fiber length when injecting a certain laser power. Additional studies need to investigate the influence of the temperature and the dose rate on the PB effects since these parameters were fixed during all the reported acquisitions.