Neutron stars can capture asymmetric dark matter (ADM), which affects the
neutron star's measurable properties and makes compact objects prime targets to
search for ADM. In this work, we use Bayesian inference to explore potential
neutron star mass-radius measurements, from current and future X-ray
telescopes, to constrain the bosonic ADM parameters for the case where bosonic
ADM has accumulated in the neutron star interior. We find that the high bosonic
ADM particle mass ($m_\chi$) and low effective self-interaction strength
($g_\chi/m_\phi)$ regime is disfavored due to the observationally and
theoretically motivated constraint that neutron stars must have at least a mass
of $1 \, \mathrm{M_\odot}$. However, within the remaining parameter space,
$m_\chi$ and $g_\chi/m_\phi$ are individually unconstrained. On the other hand,
the ADM mass-fraction, i.e., the fraction of ADM mass inside the neutron star,
can be constrained by such neutron star measurements. The inclusion of bosonic
ADM in neutron star cores also relaxes the constraints on the baryonic equation
of state space and suggests that ADM should be taken into account when
interpreting constraints from mass-radius measurements.
