Control over the bubble growth rates forming on the electrodes of water-splitting cells or chemical reactors is critical with respect to the attainment of higher energy efficiencies within these devices. This study focuses on the diffusion-driven growth dynamics of a succession of H2 bubbles generated at a flat silicon electrode substrate. Controlled nucleation is achieved by means of a single nucleation site consisting of a hydrophobic micropit etched within a micrometer-sized pillar. In our experimental configuration of constant-current electrolysis, we identify gas depletion from (i) previous bubbles in the succession, (ii) unwanted bubbles forming on the sidewalls, and (iii) the mere presence of the circular cavity where the electrode is being held. The impact of these effects on bubble growth is discussed with support from numerical simulations. The time evolution of the dimensionless bubble growth coefficient, which is a measure of the overall growth rate of a particular bubble, of electrolysis-generated bubbles is compared to that of CO2 bubbles growing on a similar surface in the presence of a supersaturated solution of carbonated water. For electrolytic bubbles and under the range of current densities considered here (5-15 A/m2), it is observed that H2 bubble successions at large gas-evolving substrates first experience a stagnation regime, followed by a fast increase in the growth coefficient before a steady state is reached. This clearly contradicts the common assumption that constant current densities must yield time-invariant growth rates. Conversely, for the case of CO2 bubbles, the growth coefficient successively decreases for every subsequent bubble as a result of the persistent depletion of dissolved CO2.