  We study the time dependent spectra produced via the bulk Compton process by
a cold, relativistic shell of plasma moving (and accelerating) along the jet of
a blazar, scattering on external photons emitted by the accretion disc and
reprocessed in the broad line region. Bulk Comptonization of disc photons is
shown to yield a spectral component contributing in the far UV band, and would
then be currently unobservable. On the contrary, the bulk Comptonization of
broad line photons may yield a significant feature in the soft X-ray band. Such
a feature is time-dependent and transient, and dominates over the non thermal
continuum only when: a) the dissipation occurs close to, but within, the broad
line region; b) other competing processes, like the synchrotron self-Compton
emission, yield a negligible flux in the X-ray band. The presence of a bulk
Compton component may account for the X-ray properties of high redshift blazars
that show a flattening (and possibly a hump) in the soft X-rays, previously
interpreted as due to intrinsic absorption. We discuss why the conditions
leading to a detectable bulk Compton feature might be met only occasionally in
high redshift blazars, concluding that the absence of such a feature in the
spectra of most blazars should not be taken as evidence against
matter--dominated relativistic jets. The detection of such a component carries
key information on the bulk Lorentz factor and kinetic energy associated to
(cold) leptons.
