  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 is 61.0 +/- 0.8 ms in the 25 -
50 keV energy range and 72 +/- 5 ms in the 50 - 100 keV band. The residual time
delay from 10 to 240 s following the start of the burst is 18.1 +/- 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).
