Nuclear magnetic resonance (NMR) investigations of the ionic liquid (IL) 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (BmpyrTFSI) are presented. BmpyrTFSI is one of the most commonly used electrolytes, either as a pure liquid or in combination with other solvents and salts. We have studied its physicochemical properties by NMR diffusion, which allows us to measure independently the self-diffusion coefficients of both anions and cations: 1H for the bmpyr + cation, 19F for the TFSI anion and 13C for both ions. The purity of the test liquid was verified by NMR spectroscopy and it was shown that there were no impurity lines in the spectra on the 1H and 13C nuclei. Self-diffusion coefficients of the cation and anion were measured in the temperature range of 243 to 333 K, which were used to study the mobility of the ions for comparison with the ionic conductivity. All the diffusion attenuations are described by a single component; we can conclude that neither ion pairs nor more complex conglomerates are observed in our system. We believe that the conductivity is completely determined by the self-diffusion of the ions. In addition, the agreement of our data with literature data on the temperature dependence of self-diffusion coefficients on the values of viscosity and ionic conductivity is considered. It is shown that the Stokes–Einstein relation is a poor description of the molecular mobility of this IL.