Longitudinal nonreciprocal charge transport is usually associated with broken time-reversal symmetry, either from magnetic order or an external magnetic field. Here, we show that it can also arise in nonmagnetic conductors preserving time-reversal symmetry through disorder-induced asymmetric scattering. Within a semiclassical Boltzmann theory, skew-scattering and side-jump processes generate a finite longitudinal current quadratic in the electric field. Our symmetry analysis identifies 42 point groups that allow this longitudinal nonreciprocal response. As a concrete example, gated Bernal-stacked bilayer graphene shows a gate-tunable nonreciprocal response with clear enhancement near its Lifshitz transition. These results identify disorder-driven asymmetric scattering as a route to bulk longitudinal nonreciprocal charge transport in crystalline conductors.