Outbursts from cataclysmic variables, such as dwarf novae (DNe), are prevalent throughout the galaxy and are known to emit strongly in the ultraviolet (UV). However, the UV emission of DN outbursts has not been studied extensively compared with the optical. Characterising in detail the physical processes responsible for outburst behaviour requires further UV data, since the UV probes the inner regions of the accretion disk. Here we report, as part of our recently launched Transient UV Objects Project (TUVO), the discovery of TUVO-21acq, a new transient which we detected in the UV using data from the Ultraviolet Optical Telescope (UVOT) aboard Swift. We detected two separate outbursts and used the UVOT data to constrain source properties, focusing on the amplitudes and timescales of the outbursts. We found that during the first outburst the source increased in brightness by at least 4.1, 2.4, and 3.5 magnitudes and during the second outburst by 4.4, 3.4, and 3.6 magnitudes in the UVW1, UVM2, and UVW2 bands, respectively. The outburst durations were in the range 6-21 days and 11-46 days, and we determined an upper limit for the recurrence time of 316 days. To further characterise the source, we obtained an optical spectrum during quiescence with SALT. The spectrum exhibited hydrogen Balmer series and helium emission lines, and a flat overall spectral shape. We confirm the nature of the source as an accreting white dwarf which underwent DN outburst based on photometric and spectroscopic properties. This study serves as a proof-of-concept for the TUVO project strategy, demonstrating that it has the capability of discovering and classifying new, interesting UV transients. We also discuss the implications of our findings for our understanding of the physics underlying DN outbursts, in particular with respect to the UV emission. We examine the need for simultaneous UV and optical observations during the onset of DN outbursts in order to help answer remaining questions, for example in the characteristics and implications of the UV delay.