The hard X-ray bursts observed during both major outbursts of the Bursting Pulsar ( GRO J1744 - 28 ) show pulsations near the neutron star spin frequency with an enhanced amplitude relative to that of the persistent emission . Consistent with previous work , we find that the pulsations within bursts lag behind their expected arrival times based upon the persistent pulsar ephemeris . For an ensemble of 1293 bursts recorded with the Burst and Transient Source Experiment , the average burst pulse time delay ( \Delta t _ { FWHM } ) is 61.0 \pm 0.8 ms in the 25 – 50 keV energy range and 72 \pm 5 ms in the 50 – 100 keV band . The residual time delay ( \Delta t _ { resid } ) from 10 to 240 s following the start of the burst is 18.1 \pm 0.7 ms ( 25 – 50 keV ) . A significant correlation of the average burst time delay with burst peak flux is found . Our results are consistent with the model of the pulse time lags presented by Miller ( 1996 ) .