For the practical use of femtosecond laser ablation, inputs of higher laser intensity are preferred to attain high-throughput material removal. However, the use of higher laser intensities for increasing ablation rates can have detrimental effects on ablation quality due to excess heat generation and air ionization. This paper employs ablation using BiBurst femtosecond laser pulses, which consist of multiple bursts (2 and 5 bursts) at a repetition rate of 64 MHz, each containing multiple intra-pulses (2–20 pulses) at an ultrafast repetition rate of 4.88 GHz, to overcome these conflicting conditions. Ablation of silicon substrates using the BiBurst mode with 5 burst pulses and 20 intra-pulses successfully prevents air breakdown at packet energies higher than the pulse energy inducing the air ionization by the conventional femtosecond laser pulse irradiation (single-pulse mode). As a result, ablation speed can be enhanced by a factor of 23 without deteriorating the ablation quality compared to that by the single-pulse mode ablation under the conditions where the air ionization is avoided.