Theoretical calculations on the dynamics of asymptotic bubble growth in an initially nonuniform concentration field are performed. A significant simplification is achieved by noting that the Jakob number for mass transfer is usually small so that the convective transport can be neglected in comparison with the diffusive transport. Numerical solutions are obtained for the growth rate of a hemispherical bubble on a surface with linear and exponential initial concentration fields of the supersaturated gas in the diffusion boundary layers and also for the cases involving concentration fields resulting from the constant interfacial concentration and the constant mass flux experiments.