  Action-based dynamical modelling, using stars as dynamical tracers, is an
excellent diagnostic to estimate the underlying axisymmetric matter
distribution of the Milky Way. However, the Milky Way's bar causes
non-axisymmetric resonance features in the stellar disc. Using Roadmapping (an
action-based dynamical modelling framework to estimate the gravitational
potential and the stellar distribution function), we systematically quantify
the robustness of action-based modelling in the presence of a bar. We construct
a set of test-particle simulations of barred galaxies (with varying bar
properties), and apply Roadmapping to different survey volumes (with varying
azimuthal position, size) drawn from these barred models. For realistic bar
parameters, the global potential parameters are still recovered to within ~ 1 -
17 percent. However, with increasing bar strength, the best-fit values of the
parameters progressively deviate from their true values. This happens due to a
combination of radial heating, radial migration, and resonance overlap
phenomena in our bar models. Furthermore, the azimuthal location and the size
of the survey volumes play important roles in the successful recovery of the
parameters. Survey volumes along the bar major axis produce larger (relative)
errors in the best-fit parameter values. In addition, the potential parameters
are better recovered for survey volumes with larger spatial coverage. As the
Sun is located just ~ 28 - 33 degrees behind the bar's major axis, an estimate
for the bar-induced systematic bias -- as provided by this study -- is
therefore crucial for future modelling attempts of the Milky Way.
