The burst mode of accretion in massive star formation is a scenario linking the initial gravitational collapse of parent pre-stellar cores to the properties of their gravitationally unstable discs and of their accretion-driven bursts. In this study, we present a series of high-resolution 3D radiation-hydrodynamics numerical simulations for young massive stars formed out of collapsing 100M⊙ molecular cores, spinning with several values of the ratio of rotational-to-gravitational energies β =5-9\percent. The models include the indirect gravitational potential caused by disc asymmetries. We find that this modifies the barycentre of the disc, causing significant excursions of the central star position, which we term stellar wobbling. The stellar wobbling slows down and protracts the development of gravitational instability in the disc, reducing the number and magnitude of the accretion-driven bursts undergone by the young massive stars, whose properties are in good agreement with that of the burst monitored from the massive protostar M17 MIR. Including stellar wobbling is therefore important for accurate modelling disc structures. Synthetic alma interferometric images in the millimetre waveband show that the outcomes of efficient gravitational instability such as spiral arms and gaseous clumps can be detected for as long as the disc is old enough and has already entered the burst mode of accretion.