Bounce modes are plasma waves which result from the coherent bounce motion of trapped particles. Such modes can occur in mirror devices when the relative spread in electron bounce frequencies is small. When electron bounce modes have perpendicular wavelengths comparable to typical ion gyroradii and frequencies near the ion gyrofrequency or some harmonic, they couple effectively with the ions and can be destabilized by a loss‐cone ion distribution. A one‐dimensional integral dispersion equation for electron bounce modes in a mirror plasma is derived and solved numerically for the wave eigenfrequencies. Predicted threshold densities for bounce mode instabilities in the Baseball I and Baseball II devices are compared with experimental values. Good agreement is found for Baseball II, but in Baseball I the predicted thresholds are consistently below observed values.