Abstract Bouncing packets are quasi‐periodic microbursts separated by the electron bounce period. Solar Anomalous and Magnetospheric Particle Explorer observations revealed relativistic (>1 MeV) inner‐belt bouncing packets with ‘crown,’ ‘decaying,’ and ‘flat’ envelopes. We test whether ducted lightning‐generated whistlers (LGWs) produce these evolutions through frequency dispersion and extended field‐aligned propagation. We use a quasilinear precipitation model driven by pitch angle diffusion from ducted LGWs (100 Hz–10 kHz), with storm‐time Colorado Inner Radiation Belt Experiment observations at L = 2 specifying the initial relativistic electron distribution. The simulations reproduce the observed shapes and relative burst amplitudes. LGW dispersion naturally produces a dual‐component signature: an impulsive, bounce‐phase‐bunched burst component and a smooth component from interactions with stretched, long‐duration LGWs. The smooth component dominates total flux, so baseline removal may underestimate precipitation.