A foreseen feature of the Molten Salt Fast Reactor is the adoption of a bubbling system for the removal of gaseous and metallic fission products (FPs). This mechanism injects helium bubbles into the core to remove FPs from the salt through floating and mass transfer mechanisms for metallic and gaseous FPs, respectively. The present work is aimed at analyzing this helium bubbling system, focusing on gaseous FPs. We investigate both operational and safety-related features in order to get information useful for the design and to assess the convenience of its adoption. Accordingly, our investigations split into two strands: (1) analyzing the characteristics of the bubbling system itself and (2) assessing the safety features of the reactor in its presence. In order to perform the above analyses, we add the capability to simulate production, transport, and mass transfer of an arbitrary number of gaseous FPs to a preexisting multiphysics solver, built with the OpenFOAM suite. In terms of operational characterization, our analyses quantify the removal efficiency through a characteristic removal time and estimate the poisoning effect of gaseous FPs. In addition, we evaluate the activity and decay heat of the removed gas, which is an aspect crucial for the design of the off-gas unit, and the effect of the bubbling system on the power versus the fuel mass flow rate curve, which is a possible control mechanism. Among our safety-related studies, we first evaluate the void coefficient, determining upper bounds on the helium flow rate in order to avoid prompt supercriticality in case of prompt loss of helium injection. The latter accidental scenario is also analyzed considering the thermal-hydraulic dynamics of the system. We also discuss another accident: complete loss of helium removal.