We present a pilot study on the nearby massive galaxy NGC 1291, in which we aim to constrain the dark matter in the inner regions, by obtaining a dynamical determination of the disc mass-to-light ratio (M/L). To this aim, we model the bar-induced dust lanes in the galaxy, using hydrodynamic gas response simulations. The models have three free parameters, the M/L of the disc, the bar pattern speed and the disc height function. We explore the parameter space to find the best fit models, i.e. those in which the morphology of the shocks in the gas simulations matches the observed dust lanes. The best-fit models suggest that the M/L of NGC 1291 agrees with that predicted by stellar population synthesis models in the near-infrared (≈ 0.6 M⊙/L⊙), which leads to a borderline maximum disc for this galaxy. The bar rotates fast, with corotation radius ⩽ 1.4 times the bar length. Additionally, we find that the height function has a significant effect on the results, and can bias them towards lower or higher M/L.