A popular method to induce synthetic propulsion at the microscale is to use the forces created by surface-produced gas bubbles inside the asymmetric body of a catalytic swimmer (referred to in the literature as microrocket). Gas bubbles nucleate and grow within the swimmer and migrate toward one of its openings due to asymmetric geometric confinement, generating a net hydrodynamic force which propels the device. Here, numerical simulations are used to develop a joint chemical (diffusive) and hydrodynamic (Stokes) analysis of the bubble growth within a conical catalytic microrocket and of the associated bubble and microrocket motion. With this computational model, the bubble dynamics are solved for over one bubble cycle ranging from its nucleation to its exiting the conical rocket, and the propulsion characteristics are identified as a function of all design parameters (geometry and chemical activity of the motor, surface tension, physicochemical constants). The results suggest that hydrodynamics and chemistry partially decouple in the motion of the bubbles, with hydrodynamics determining the distance travelled by the microrocket over each cycle while chemistry sets the bubble ejection frequency. This numerical model allows for the identification of an optimal microrocket shape and size for which the distance travelled per cycle duration is maximized.