In this work, we report on observations with the Neutron Star Interior Composition Explorer of the known neutron star X-ray transient XTE J1739-285. We observed the source in 2020 February and March, finding it in a highly active bursting state. Across a 20 day period, we detected 32 thermonuclear X-ray bursts, with an average burst recurrence time of 2.0(-0.3)(+0.)4. A timing and spectral analysis of the ensemble of X-ray bursts reveals homogeneous burst properties, evidence for short-recurrence time bursts, and the detection of a 386.5 Hz burst oscillation candidate. The latter is especially notable, given that a previous study of this source claimed a 1122 Hz burst oscillation candidate. We did not find any evidence of variability near 1122 Hz and instead find that the 386.5 Hz oscillation is the more prominent signal of the two burst oscillation candidates. Hence, we conclude it is unlikely that XTE J1739-285 has a submillisecond rotation period.