We study the role of bulk-surface exchange in the density relaxation kinetics and self-diffusion of surface-active molecules at liquid surfaces. In «strongly adsorbing» systems, relaxation occurs through bulk-mediated effective surface diffusion characterized by one-step distributions with long tails; molecules execute Levy walks on the surface. Correspondingly, at times before particles are finally lost to the bulk, surface displacement r is non-Fickian and exhibits anomalous scaling: moments grow as ∼t ζ(q) , where ζ(q)=q for q 1 and ∼t ln t. The width of an initially localized density disturbance increases linearly in time with a «speed» c which is universally related to other observables. Numerical simulations confirm the family of exponents ζ (q), and reproduce the observable c. We consider a simple example where end-functionalised macromolecules adsorb at a solid surface, finding c∼1/s where s is the surface «stickiness» parameter. At liquid-fluid interfaces viscoelastic effects compete. For sub-micron scales, we argue that self-diffusion will typically remain dominated at high coverages by the anomalous bulk-mediated mechanism, while surface viscoelasticity will dominate the relaxation of density perturbations