Time-resolved X-ray magnetic circular dichroism under the effects of ferromagnetic resonance (FMR), known as X-ray ferromagnetic resonance (XFMR) measurements, enables direct detection of precession dynamics of magnetic moment. Here we demonstrated XFMR measurements and Bayesian analyses as a quantitative probe for the precession of spin and orbital magnetic moments under the FMR effect. Magnetization precessions in two different Pt/Ni-Fe thin film samples were directly detected. Bayesian analyses of the XFMR energy spectra around the Ni L2,3 absorption edges reveal the different direction of the precession axis of spin and orbital moments. This different dynamical behaviors of spin and orbital moments can be attributed to the perpendicular magnetic anisotropy on the orbital moment in Pt/Ni-Fe thin films. Our study paves the way for a microscopic investigation of the contribution of the orbital magnetic moment to magnetization dynamics.