GS 0836–429 is a neutron star X-ray transient that displays Type-I X-ray bursts. In 2003 and 2004 it experienced two outbursts in X-rays. We present here an analysis of the system’s bursting properties during these outbursts. We studied the evolution of the 2003–2004 outbursts in soft X-rays using RXTE (2.5–12 keV; ASM) and in hard X-rays with INTEGRAL (17–80 keV, IBIS/ISGRI). Using data from the JEM-X monitor onboard INTEGRAL, we studied the bursting properties of the source. We detected 61 Type-I X-ray bursts during the 2004 outburst and confirm that the source displayed a quasi-periodic burst recurrence time of about 2.3 h. We improve the characterisation of the fuel composition, as well as the description of the typical burst durations and fluences. We estimate the average value of α to be 49 ± 3, which describes the ratio of the gravitational energy released between bursts to the nuclear energy released in an X-ray burst. Both this value and the observed burst profiles indicate a regime of a mixed He/H runaway triggered by unstable helium ignition. In addition, we report the detection of four series of double bursts, with burst recurrence times of ≤20 min. The secondary bursts are always shorter and less energetic than the primary and typical bursts from the source. The measured recurrence time in double bursts is too short to allow the accretion of enough fresh material, which is needed to trigger a Type-I X-ray burst. This suggests the presence of leftover, unburned material from the preceding burst, which gets ignited on a time scale of minutes. The energies and time scales of the secondary bursts suggest a lower fraction of hydrogen compared to that estimated for the primary bursts. The persistent emission was roughly constant during the period when the Type I X-ray bursts were detected. We derive an average accretion rate during our observations of ṁ ~ 8% ṁEdd. The spectrum of the persistent emission during these observations can be fit with a non-thermal component, indicative for the source to be in a hard state when the INTEGRAL observations were performed.