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The bulk photovoltaic effect in noncentrosymmetric materials is an intriguing physical phenomenon that holds potential for high-efficiency energy harvesting. Here, we study the shift current bulk photovoltaic effect in the transition-metal dichalcogenide MoS₂. We present a simple automated method to guide materials design and use it to uncover a distortion to monolayer 2H-MoS₂ that dramatically enhances the integrated shift current. Using this distortion, we show that overlap in the Brillouin zone of the distributions of the shift vector (a quantity measuring the net displacement in real space of coherent wave packets during excitation) and the transition intensity is crucial for increasing the shift current. The distortion pattern is related to the material polarization and can be realized through an applied electric field via the converse piezoelectric effect. This finding suggests an additional method for engineering the shift current response of materials to augment previously reported methods using mechanical strain.