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We continue our systematic statistical study of various components of gamma-ray burst (GRB) optical light curves. We decompose the early onset bump and the late re-brightening bump with empirical fits and analyze their statistical properties. Among the 146 GRBs that have well-sampled optical light curves, the onset and re-brightening bumps are observed in 38 and 26 GRBs, respectively. It is found that the typical rising and decaying slopes for both the onset and re-brightening bumps are ~1.5 and ~-1.15, respectively. No early onset bumps in the X-ray band are detected to be associated with the optical onset bumps, while an X-ray re-brightening bump is detected for half of the re-brightening optical bumps. The peak luminosity is anti-correlated with the peak time Lp α t -1.81±0.32 p for the onset bumps and Lp ℵ t -0.83±0.17 p for the re-brightening bumps. Both Lp and the isotropic energy release of the onset bumps are correlated with Eγ,iso, whereas no similar correlation is found for the re-brightening bumps. These results suggest that the afterglow onset bumps are likely due to the deceleration of the GRB fireballs. Taking the onset bumps as probes for the properties of the fireballs and their ambient medium, we find that the typical power-law index of the relativistic electrons is 2.5 and the medium density profile behaves as n ℵ r -1 within the framework of the synchrotron external shock models. With the medium density profile obtained from our analysis, we also confirm the correlation between the initial Lorentz factor (Γ0) and Eiso,γ in our previous work. The jet component that produces the re-brightening bump seems to be on-axis and independent of the prompt emission jet component. Its typical kinetic energy budget would be about one order of magnitude larger than the prompt emission component, but with a lower Γ0, typically several tens. [ABSTRACT FROM AUTHOR]