  Bulk flow velocities are typically estimated in the idealised picture where
observers are moving within a perfectly homogeneous and isotropic space-time.
This picture is consistent within standard perturbation theory up to
relativistic effects that lead to correction terms of order $v z$, where $z$ is
the redshift of observation, and $v$ is the amplitude of the bulk flow. The
dominant relativistic contributions at scales $z \lesssim 1$ are caused by
gravitational redshift and time evolution of the velocity field. We include
these effects within a broadly applicable weak-field approximation, and provide
a cosmographic formula for estimating bulk flows at a high precision. Based on
this formula, we judge that recent bulk flow estimates are biased toward larger
values by $\sim 10\%$. This theoretical bias surpasses the measurement biases
of the same estimates, and it will become still more important to account for
the relativistic effects as the scales at which bulk flows are estimated to
increase.
