The strength of a deep layered rock mass depends on both bedding orientation and the three-dimensional stress direction. Their combined influence over a complete deviatoric section at constant stress level (I₁), however, remains insufficiently resolved. This study investigates a rock mass containing one set of parallel persistent bedding planes with a fixed dip direction of 90°. Five bedding dips and 36 generalized Lode angles (Θ) were examined, giving 180 stress paths at I₁ = 180 MPa. Each path increased the deviatoric stress amplitude while keeping I₁ and Θ constant. The numerical matrix followed the smooth generalized Zhang–Zhu (GZZ) criterion, and the cohesionless bedding planes followed the Mohr–Coulomb law. A closed-form threshold was also derived for frictional sliding along the bedding. The resulting envelopes for complementary dips were mirror images, while the 45° envelope was self-symmetric. At Θ = 90°, bedding shear traction vanished and all five dips failed under matrix control. In the 110 joint-controlled cases, the numerical strength and analytical sliding threshold differed by only 0.66% on average and 2.58% at most. Bedding reduced the minimum strength to approximately 33% of the matrix strength, with the greatest reduction at intermediate dips. These results show that the smaller of the matrix strength and bedding sliding threshold captures both the strength envelope and the transition between the two controlling mechanisms.