We probe electron and hole mobilities in bilayer graphene under exposure to molecular oxygen. We find that the adsorbed oxygen reduces electron mobilities and increases hole mobilities in a reversible and activated process. Our experimental results indicate that hole mobilities increase due to the screening of long-range scatterers by oxygen molecules trapped between the graphene and the substrate. First principle calculations show that oxygen molecules induce resonant states close to the charge neutrality point. Electron coupling with such resonant states reduces the electron mobilities, causing a strong asymmetry between electron and hole transport. Our work demonstrates the importance of short-range scattering due to adsorbed species in the electronic transport in bilayer graphene on SiO2 substrates.