  Inferring cosmological parameters from time-delay strong lenses requires a
significant investment of telescope time; it is therefore tempting to focus on
the systems with the brightest sources, the highest image multiplicities and
the widest image separations. We investigate if this selection bias can
influence the properties of the lenses studied and the cosmological parameters
that are inferred. Using a population of lenses with ellipsoidal powerlaw
density profiles, we build a sample of double and quadruple image systems.
Assuming reasonable thresholds on image separation and flux, based on current
lens monitoring campaigns, we find that the typical density profile slopes of
monitorable lenses are significantly shallower than the input ensemble. From a
sample of quadruple image lenses we find that this selection function can
introduce a 3.5% bias on the inferred time-delay distances if the ensemble of
deflector properties is used as a prior for a cosmographical analysis. This
bias remains at the 2.4% level when high resolution imaging of the quasar host
is used to precisely infer the density profiles of individual lenses. We also
investigate if the lines-of-sight for monitorable strong lenses are biased.
After adding external convergence, $\kappa$, and shear to our lens population
we find that the expectation value for $\kappa$ is increased by 0.004 and 0.009
for doubles and quads respectively. $\kappa$ is degenerate with the value of
$H_0$ inferred from time delays; fortunately the shift in $\kappa$ only induces
a 0.9 (0.4) percent bias on $H_0$ for quads (doubles). We therefore conclude
that whilst the properties of typical quasar lenses and their lines-of-sight do
deviate from the global population, the total magnitude of this effect is
likely a subdominant effect for current analyses, but has the potential to be a
major systematic for samples of $\sim$25 or more lenses.
