Particle–fluid hybrid simulations of electrostatic ion‐cyclotron instabilities in a mirror plasma have been extended to include axial ion bouncing in a nonuniform magnetic field. This model admits unstable ion‐bounce modes as well as drift‐cyclotron and drift‐cyclotron‐loss‐cone modes. Linear theory showed that ion‐bounce modes were as difficult to stabilize as drift‐cyclotron‐loss‐cone modes, but the ion‐bounce modes saturated at very low levels in simulations. Simulations have also followed the self‐consistent interaction of a mirror plasma with turbulent electric fields in the presence of warm plasma stream, ion drag on electrons, injection of energetic neutral beams, and transit losses. Driven by velocity diffusion due to the drift‐cyclotron‐loss‐cone instability, the plasma evolved to a stable configuration. The wave turbulence was moderated by streaming plasma and axial electron dissipation, was insensitive to the energy width of the neutral beam, and decayed when the neutral beam was removed. The simulation results confirmed many of the predictions of quasilinear theory and theories of orbital stochasticity, and were in qualitative agreement with many (but not all) of the observations in the Lawrence Livermore National Laboratory 2XIIB experiment.