We investigate ion dynamics under pressure in the ionic liquid 1-butyl-1-methylpyrrolidinium bis[oxalate]borate (BMP-BOB) by conductivity relaxation measurements in the temperature range 123-300 K and varying pressures from 0.1 MPa up to 0.5 GPa. We report on the influence of pressure on the relaxation times and on the spectral shape of the conductivity relaxation process. We also analyze the pressure dependence of the glass transition temperature and find that the dynamic response under pressure in this ionic liquid shows remarkable similarities to nonionic glass formers. The main relaxation process shows temperature-pressure superposition while a secondary relaxation process, very weakly depending on pressure, is observed. The spectral shape of the main relaxation broadens with increasing pressure or decreasing temperature, but is found to be the same when the relaxation time is the same, independently of the particular pressure and temperature values.