  We present a systematic study of line widths in the [\ion{O}{3}]$\lambda$5007
and H$\alpha$ lines for a sample of 86 planetary nebulae in the Milky Way bulge
based upon spectroscopy obtained at the \facility{Observatorio Astron\'omico
Nacional in the Sierra San Pedro M\'artir (OAN-SPM)} using the Manchester
Echelle Spectrograph. The planetary nebulae were selected with the intention of
simulating samples of bright extragalactic planetary nebulae. We separate the
planetary nebulae into two samples containing cooler and hotter central stars,
defined by the absence or presence, respectively, of the \ion{He}{2}
$\lambda$6560 line in the H$\alpha$ spectra. This division separates samples of
younger and more evolved planetary nebulae. The sample of planetary nebulae
with hotter central stars has systematically larger line widths, larger radii,
lower electron densities, and lower H$\beta$ luminosities. The distributions of
these parameters in the two samples all differ at significance levels exceeding
99%. These differences are all in agreement with the expectations from
hydrodynamical models, but for the first time confirmed for a homogeneous and
statistically significant sample of galactic planetary nebulae. We interpret
these differences as evidence for the acceleration of the nebular shells during
the early evolution of these intrinsically bright planetary nebulae. As is the
case for planetary nebulae in the Magellanic Clouds, the acceleration of the
nebular shells appears to be the direct result of the evolution of the central
stars.
