We present the results of our broadband spectral analysis of 42 SGR J1550−5418 bursts simultaneously detected with the Swift/X-ray Telescope (XRT) and the Fermi/Gamma-ray Burst Monitor (GBM), during the 2009 January active episode of the source. The unique spectral and temporal capabilities of the XRT windowed timing mode have allowed us to extend the GBM spectral coverage for these events down to the X-ray domain (0.5–10 keV). Our earlier analysis of the GBM data found that the SGR J1550−5418 burst spectra were described equally well with either a Comptonized model or with two blackbody functions; the two models were statistically indistinguishable. Our new broadband (0.5–200 keV) spectral fits show that, on average, the burst spectra are better described with two blackbody functions than with the Comptonized model. Thus, our joint XRT–GBM analysis clearly shows for the first time that the SGR J1550−5418 burst spectra might naturally be expected to exhibit a more truly thermalized character, such as a two-blackbody or even a multi-blackbody signal. Using the Swift and RXTE timing ephemeris for SGR J1550−5418 we construct the distribution of the XRT burst counts with spin phase and find that it is not correlated with the persistent X-ray emission pulse phase from SGR J1550−5418. These results indicate that the burst emitting sites on the neutron star need not to be co-located with hot spots emitting the bulk of the persistent X-ray emission. Finally, we show that there is a significant pulse phase dependence of the XRT burst counts, likely demonstrating that the surface magnetic field of SGR J1550−5418 is not uniform over the emission zones, since it is anticipated that regions with stronger surface magnetic field could trigger bursts more efficiently.