We report direct measurements of the magnetic field screening at the limits of the Meissner phase for two superconducting Nb samples. The samples are processed with two different surface treatments that have been developed for superconducting radio-frequency cavity applications -- a "baseline" treatment and an oxygen-doping ("O-doping") treatment. The measurements show: 1) that the screening length is significantly longer in the "O-doping" sample compared to the "baseline" sample; 2) that the screening length near the limits of the Meissner phase increases with applied field; 3) the evolution of the screening profile as the material transitions from the Meissner phase to the mixed phase; and 4) a demonstration of the absence of any screening profile for the highest applied field, indicative of the full flux entering the sample. Measurements are performed utilizing the $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) technique that allows depth resolved studies of the local magnetic field within the first 100 nm of the surface. The study takes advantage of the $\beta$-SRF beamline, a new facility at TRIUMF, Canada, where field levels up to 200 mT are available parallel to the sample surface to replicate radio frequency (RF) fields near the Meissner breakdown limits of Nb.
