We present an extensive study of angle-dependent transverse magnetoresistance in bismuth, with a magnetic field perpendicular to the applied electric current and rotating in three distinct crystallographic planes. The observed angular oscillations are confronted with the expectations of semiclassic transport theory for a multivalley system with anisotropic mobility and the agreement allows us to quantify the components of the mobility tensor for both electrons and holes. A quadratic temperature dependence is resolved. As Hartman argued long ago, this indicates that inelastic resistivity in bismuth is dominated by carrier-carrier scattering. At low temperature and high magnetic field, the threefold symmetry of the lattice is suddenly lost. Specifically, a 2π/3 rotation of magnetic field around the trigonal axis modifies the amplitude of the magnetoresistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we map the boundary in the (field, temperature) plane separating two electronic states. In the less symmetric state, confined to low temperature and high magnetic field, the three Dirac valleys cease to be rotationally invariant. We discuss the possible origins of this spontaneous valley polarization, including a valley-nematic scenario.