Ultrafast laser inscription (ULI) inside semiconductors offers new perspectives for 3D monolithic structures to be fabricated and new functionalities to be added in electronic and photonic microdevices. However, important challenges remain because of nonlinear effects such as strong plasma generation that distort the energy delivery at the focal point when exposing these materials to intense infrared light. Up to now, the successful technological demonstrations have primarily concentrated on silicon (Si). In this paper, we target at another important semiconductor: gallium arsenide (GaAs). With nonlinearities higher than those of Si, 3D-machining of GaAs with femtosecond pulses becomes even harder. However, we show that the difficulty can be circumvented by burst-mode irradiation. We generate and apply trains of pulses at terahertz repetition rates for efficient pulse-to-pulse accumulation of laser-induced free carriers in the focal region, while avoiding an overdose of prefocal excitations. The superior performance of burst-mode irradiation is confirmed by a comparative study conducted with infrared luminescence microscopy. The results indicate a successful reduction of the plasma density in the prefocal region so that higher pulse energy reaches the focal spot. The same method is applied to identify optimum irradiation conditions considering particular cases such as asymmetric pulse trains and aberrated beams. With 64-pulse trains, we successfully manage to cross the writing threshold providing a solution for ULI inside GaAs. The application potential is finally illustrated with a stealth dicing demonstration by taking benefit of the burst mode. The irradiation method opens wide possibilities for 3D structuring inside GaAs by ULI.