We have designed a peptide with switchable surface activity, where the folded (alpha-helical) form of the peptide is amphiphilic and the unfolded form is not. To understand the factors influencing the dynamics of the switchability, a model is developed for the transport of the surface active form of the peptide from the solution onto air-water interface. As is the case with the low molecular weight head-tail surfactants, the transport involves the bulk diffusion of the folded form to the surface and the kinetic adsorption onto the interface. Unlike the head-tail surfactants, the diffusion can be augmented by the kinetics of the folding of the peptide from the unfolded form. The model is formulated within the context of the transport of the peptide from a uniform bulk solution onto an initially clean air-water interface in a pendant bubble system, where the transport rate can be measured by recording the reduction in surface tension using the shape analysis of the bubble. Experiments are undertaken and compared to the predictions of the model simulations of the tension reduction for a range of values of the kinetic adsorption constant and the folding kinetic constant. The results indicate that the kinetic adsorption rate of the folded peptide onto air-water interface dominates the dynamic process, which contrasts many head-tail surfactants where diffusion typically dominates over kinetics adsorption. Moreover, our 'best-fits' suggest that there is a phase transition at high surface concentrations that slows the long-time adsorption of the peptides to the interface. Finally, the numerical solution is compared with an asymptotic solution, showing agreement with our findings that the fundamental dynamics of the tunable surface-active peptide are indeed controlled by the adsorption step.