Context.Swift J1910.2–0546 (=MAXI J1910‑057) is a Galactic X-ray transient discovered during a bright outburst in 2012. Its X-ray spectral and timing properties point to a black-hole accretor, yet the orbital period remains uncertain, and no reliable dynamical constraints on the binary parameters are available. The 2012 event, extensively monitored at X-ray and optical wavelengths, offers a rare opportunity to investigate the structure and dynamics of the system and to constrain its fundamental properties. Aims. We use time-series optical photometry and spectroscopy, obtained during outburst and quiescence, to estimate the orbital period, characterise the donor star, determine the interstellar extinction, distance, and system geometry, and constrain the component masses. Methods. Multi-site r-band and clear-filter light curves and WHT/ACAM spectra from the 2012 outburst were combined with time-series spectroscopy from GTC/OSIRIS and VLT/FORS2 in quiescence. Period searches were conducted using generalised Lomb–Scargle, phase-dispersion minimisation, and analysis-of-variance algorithms. We used diffuse interstellar bands to constrain E(B ‑ V), while empirical correlations involving Hα yielded estimates of K2, q, and i. Results. We detected a coherent, double-humped modulation with a period of 0.0941 ± 0.0007 d (2.26 ± 0.02 h) during the outburst. Its morphology is consistent with an early superhump, suggesting that the true orbital period may be slightly shorter than 4.52 h. The Hα radial velocity curves do not yield a definitive orbital period. In quiescence, TiO bands indicate an M3‑M3.5 donor contributing ≃70% of the red continuum. Diffuse interstellar bands give E(B ‑ V) = 0.60 ± 0.05 and NH = (3.9 ± 1.3)×1021 cm‑2, placing the system at a distance of 2.8‑4.0 kpc. The Hα line width in quiescence (FWHM0 = 990 ± 45 km s‑1), via a FWHM–K2 calibration, provides an estimate of K2, while its double-peaked profile gives q and the orbital inclination. The latter appears much higher than estimates from X-ray studies. Adopting the resulting K2 = 230 ± 17 km s‑1 and q = 0.032 ± 0.010, along with two orbital period scenarios (2.25 and 4.50 h), Monte Carlo sampling returns a compact object mass of M1 = 8 ‑ 11 M⊙ and an inclination of i = 13° ‑18° for plausible donor masses (M2 = 0.25 ‑ 0.35 M⊙). Overall, we favour an orbital period of 4.5 h. Conclusions.Swift J1910.2–0546 may be a short-period, low-inclination black hole X-ray transient, although the possibility of it being a neutron star accretor cannot be completely ruled out. Subsequent phase-resolved spectroscopy and photometry during quiescence are needed to better determine its fundamental parameters.