  We continue our systematic statistical study of various components in
gamma-ray burst (GRB) optical lightcurves. 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
lightcurves, 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, L_p\propto t_{p}^{-1.81+/-0.32} and L_p\propto t_{p}^{-0.83+/-0.17}
for the onset and re-brightening bumps, respectively. Both L_p and the
isotropic energy release of the onset bumps are correlated with E_{\gamma,
iso}, whereas no similar correlation is found for the re-brightening bumps.
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\propto 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 initial Lorentz factor (\Gamma_0) and E_{\gamma, iso} 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 \Gamma_0, typically several tens.
