When you use Henry's law it's implicit that you have dynamic equilibrium at the interface gas phase/liquid phase.
For a steady-state case I would do the following:
If you assume the air to behave as an ideal gas, you can find it's molar concentration in the gas phase by using the equation of state (ideal gas law). With this concentration, you use the Henry's law to find the concentration of air dissolved in your liquid water at the interface gas phase/liquid water phase. You can now apply a mass balance in the liquid water dormain where you just include both diffusive and convective flux terms to find the spatial distribution of dissolved air in your liquid water phase.
For a transient case, I would review the behaviour at gas/liquid interface and just add the transient term to the mass balance expression.
Hope it helps.