Current sensing is performed in a non-volatile storage device for a non-volatile storage element. A voltage is applied to a selected word line of the first non-volatile storage element, and source and p-well voltages are applied to a source and a p-well, respectively, associated with the non-volatile storage element. The source and p-well voltages are regulated at respective positive DC levels to avoid a ground bounce, or voltage fluctuation, which would occur if the source voltage at least was regulated at a ground voltage. A programming condition of the non-volatile storage element is determined by sensing a current in a NAND string of the non-volatile storage element. The sensing can occur quickly since there is no delay in waiting for the ground bounce to settle.