This study is concerned with a minimal model of a bowed string instrument, derived through a modal decomposition of the linear Kirchhoff-Carrier PDE with a Coulomb friction force that is subsequently regularized for the sake of numerical conditioning. A bifurcation analysis of the regularized model provides a cartography of the different sound regimes in the parameter space. These results are then compared with time-domain simulations of the unregularized Coulomb friction, to evaluate whether the regularized dynamics can converge to the unregularized dynamics.