During the third all-sky survey (eRASS3), eROSITA, the soft X-ray instrument aboard Spectrum-Roentgen-Gamma, detected a new hard X-ray transient, eRASSt J040515.6-745202, in the direction of the Magellanic Bridge. We arranged follow-up observations and searched for archival data to reveal the nature of the transient. Using X-ray observations with XMM-Newton, NICER, and Swift, we investigated the temporal and spectral behaviour of the source for over about 10 days. The X-ray light curve obtained from the XMM-Newton observation with an 28 ks exposure revealed a type-I X-ray burst with a peak bolometric luminosity of at least 1.4e37 erg/s. The burst energetics are consistent with a location of the burster at the distance of the Magellanic Bridge. The relatively long exponential decay time of the burst of 70 s indicates that it ignited in a H-rich environment. The non-detection of the source during the other eROSITA surveys, twelve and six months before and six months after eRASS3, suggests that the burst was discovered during a moderate outburst which reached 2.6e36 erg/s in persistent emission. During the NICER observations, the source showed alternating flux states with the high level at a similar brightness as during the XMM-Newton observation. This behaviour is likely caused by dips as also seen during the last hour of the XMM-Newton observation. Evidence for a recurrence of the dips with a period of 21.8 hr suggests eRASSt J040515.6-745202 is a low-mass X-ray binary (LMXB) system with an accretion disk seen nearly edge on. We identify a multi-wavelength counterpart to the X-ray source in UVW1 and g, r, i, and z images obtained by the optical/UV monitor on XMM-Newton and the Dark Energy Camera at the Cerro Tololo Inter-American Observatory. (abbreviated)