  Understanding the role of frictional drag in diffusive transport is an
important problem in the field of active turbulence. Using a continuum model
that applies well to bacterial suspensions, we investigate the role of Ekmann
friction on the transport of passive (Lagrangian) tracers that go with the
local flow. We find that the crossover from ballistic to diffusive regime
happens at a time scale $\tau_c$ that attains a minimum at zero friction,
meaning that both injection and dissipation of energy delay the relaxation of
tracers. We explain this by proposing that $\tau_c \sim 2
\ell^*/u_{\text{rms}}$, where $\ell^*$ is a dominant length scale extracted
from energy spectrum peak, and $u_{\text{rms}}$ is a velocity scale that sets
the kinetic energy at steady state, both scales monotonically decrease with
friction. Finally, we predict robust scaling laws for $\ell^*$,
$u_{\text{rms}}$ and the diffusion coefficient $\mathcal{D} \sim \ell^*
u_{\text{rms}} / 2$, that are valid over a wide range of fluid friction. Our
findings might be relevant to transport phenomena in a generic active fluid.
