The time profile of the fluorescence light emission of atomic hydrogen in an expanding plasma beam after pulsed excitation with a nanosecond laser is studied, both experimentally and computationally. Ground state H atoms in an expanding Ar-H cascaded arc plasma are excited to the p=3 level using two-photon laser excitation at 205 nm. The resulting fluorescence is resolved in time with a fast photomultiplier tube to investigate the occurrence of quenching. A fluorescence decay time of (10+/-0.5) ns is measured under all circumstances, indicating that there is a complete l mixing of the p=3 sublevels. A time-resolved collisional radiative model is developed to model pulsed laser induced fluorescence for a large range of plasma parameters. The model calculations agree well with the experimental results over the entire range of conditions and indicate that two-photon LIF can strongly influence the local electron and ion densities, resulting in a "self-quenching" of the laser-induced H fluorescence.