We apply the barred Schwarzschild method developed by Tahmasebzadeh et al. (2022) to a barred S0 galaxy, NGC 4371, observed by IFU instruments from the TIMER and ATLAS3D projects. We construct the gravitational potential by combining a fixed black hole mass, a spherical dark matter halo, and stellar mass distribution deprojected from 3.6 μm S$^4$G image considering an axisymmetric disc and a triaxial bar. We independently modelled kinematic data from TIMER and ATLAS3D. Both models fit the data remarkably well. We find a consistent bar pattern speed from the two sets of models with $\Omega _{\rm p} = 23.6 \pm 2.8 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$ and $\Omega _{\rm p} = 22.4 \pm 3.5 \, \mathrm{km \, s^{-1} \, kpc^{-1} }$, respectively. The dimensionless bar rotation parameter is determined to be $\mathcal {R} \equiv R_{\rm cor}/R_{\rm bar}=1.88 \pm 0.37$, indicating a likely slow bar in NGC 4371. Additionally, our model predicts a high amount of dark matter within the bar region ($M_{\rm DM}/ M_{\rm total}$$\sim 0.51 \pm 0.06$), which, aligned with the predictions of cosmological simulations, indicates that fast bars are generally found in baryon-dominated discs. Based on the best-fitting model, we further decompose the galaxy into multiple 3D orbital structures, including a BP/X bar, a classical bulge, a nuclear disc, and a main disc. The BP/X bar is not perfectly included in the input 3D density model, but BP/X-supporting orbits are picked through the fitting to the kinematic data. This is the first time a real barred galaxy has been modelled utilizing the Schwarzschild method including a 3D bar.