Periodic orbits are crucial in facilitating the understanding of the dynamical behavior of elongated asteroids. As a specific type of periodic orbit, resonant orbits can enrich the orbit design method of deep-space exploration missions. Herein, a dipole segment model for investigating the orbital dynamics of elongated asteroids is briefly introduced. A new numerical algorithm named the modified path searching method for identifying spin–orbit resonant orbits is proposed. Using the modified path searching and pseudo-arclength continuation methods, four spin--orbit resonant families for asteroid 2063 Bacchus are obtained. The distribution of eigenvalues and stability curves for the four resonant families are presented. In particular, some critical points corresponding to period-doubling and tangent bifurcations appear in the stability curves.