Dynamic wetting is known to influence the dynamics of droplets and bubbles on surfaces. In this study, we present a numerical approach to simulate the oversaturation-driven growth of single bubbles on surfaces under the influence of dynamic wetting. An existing mass transfer model implemented in the Volume of Fluid (VOF) framework Basilisk is combined with a dynamic wetting model that includes contact angle hysteresis. Motivated by the initial dominance of surface tension during bubble growth, we explore the extent to which enlarged diffusion coefficients can be used to speed up the simulations. Hereby, for calculating the instantaneous contact angle, a properly rescaled value of the contact line velocity needs to be used. An extensive validation of the simulation method is conducted, including comparisons with experimental results. The impact of dynamic wetting on bubble growth is elucidated by comparisons with the bubble behavior at static wetting.