  We revisit the effect of peculiar velocities on low-redshift type Ia
supernovae. Velocities introduce an additional guaranteed source of
correlations between supernova magnitudes that should be considered in all
analyses of nearby supernova samples but has largely been neglected in the
past. Applying a likelihood analysis to the latest compilation of nearby
supernovae, we find no evidence for the presence of these correlations,
although, given the significant noise, the data is also consistent with the
correlations predicted for the standard $\Lambda$CDM model. We then consider
the dipolar component of the velocity correlations -- the frequently studied
"bulk velocity" -- and explicitly demonstrate that including the velocity
correlations in the data covariance matrix is crucial for drawing correct and
unambiguous conclusions about the bulk flow. In particular, current supernova
data is consistent with no excess bulk flow on top of what is expected in
$\Lambda$CDM and effectively captured by the covariance. We further clarify the
nature of the apparent bulk flow that is inferred when the velocity covariance
is ignored. We show that a significant fraction of this quantity is expected to
be noise bias due to uncertainties in supernova magnitudes and not any physical
peculiar motion.
