  We investigate the impact of introducing Majorana bound states, formed by a
proximitized semiconducting nanowire in the topological regime, into a current
biased capacitive Josephson junction, thereby adding delocalized states below
the superconducting gap. We find that this qualitatively changes the charge
dynamics of the system, diminishing the role of Bloch oscillations and causing
single-particle tunnelling effects to dominate. We fully characterize the
resulting charge dynamics and the associated voltage and current signals. Our
work reveals a rich landscape of behaviours in both the static and time-varying
driving modes. This can be directly attributed to the presence of Majorana
bound states, which serve as a pathway for charge transport and enable
non-equilibrium excitations of the Majorana-Josephson device.
