Swift J1749.4-2807 is the only known eclipsing accreting millisecond X-ray pulsar. In this paper, we report on seven thermonuclear (Type-I) X-ray bursts observed by NICER during its 2021 outburst. The first six bursts show slow rises and long decays, indicative of mixed H/He fuel, whereas the last burst shows fast rise and decay, suggesting He-rich fuel. Time-resolved spectroscopy of the bursts revealed typical phenomenology (i.e. an increase in blackbody temperature during the burst rise, and steady decrease in the decay), however, they required a variable NH. We found that the values of NH during the bursts were roughly double those found in the fits of the persistent emission prior to each burst. We interpret this change in absorption as evidence of burst-disc interaction, which we observe due to the high inclination of the system. We searched for burst oscillations during each burst and detected a signal in the first burst at the known spin frequency of the neutron star (517.92 Hz). This is the first time burst oscillations have been detected from Swift J1749.4-2807. We further find that each X-ray burst occurs on top of an elevated persistent count rate. We performed time-resolved spectroscopy on the combined data of the bursts with sufficient statistics (i.e. the clearest examples of this phenomenon) and found that the blackbody parameters evolve to hotter temperatures closer to the onset of the bursts. We interpret this as a consequence of an unusual marginally stable burning process similar to that seen through mHz QPOs.