Bursts of femtosecond laser pulses were used to record internal modifications inside fused silica for selective chemical etching. Two-pulse bursts with a variable energy ratio between those pulses at a fixed inter-pulse duration of 14.5 ns were applied for the first time. The selective chemical etching rate of the laser-modified material with the burst of two pulses was compared to the single-pulse regime when etching in HF and KOH etchants. The advantage of the burst-mode processing was demonstrated when etching was performed in the KOH solution. More regular nanogratings were formed, and the etching initiation was more stable when burst pulses were applied for fused silica modification. The vertical planar structures were obtained using the two-pulse bursts with an energy ratio of 1:2, increasing the etching rate by more than 35% compared to the single-pulse processing. The highest ever reported selectivity of 1:2000 was demonstrated by introducing the two-pulse burst mode.