1. A non-volatile storage system, comprising: a set of non-volatile storage elements arranged in a plurality of NAND strings, each of the plurality of NAND strings is associated with a respective bit line, a respective sense component, and a respective discharge path; and one or more control circuits in communication with the set of non-volatile storage elements, the one or more control circuits: (1) during a first time period: (a) apply a source voltage to a source of each of the plurality of NAND strings, (b) prevent coupling of each respective bit line to the respective sense component, and (c) couple each respective bit line to the respective discharge path, and (2) during a second time period which follows the first time period, (a) continue to apply the source voltage to the source of each of the plurality of NAND strings, and allow coupling of each respective bit line to the respective sense component.