Developing organic cathodes that combine robust electrochemical performance with functional versatility is pivotal for the advancement of aqueous zinc-ion batteries (ZIBs). Herein, we design a bipolar polymer-graphene composite cathode, poly(1,8-diaminonaphthalene)-reduced graphene oxide (PDAN-rGO), through in situ polymerization on graphene sheets. The conductive graphene network and bipolar redox-active polymer synergistically enable a dual-ion storage mechanism involving both Zn²⁺ and CF₃SO₃⁻. The PDAN-rGO cathode delivers a high reversible capacity of 162.67 mAh·g⁻¹ at 0.1 A·g⁻¹, excellent rate performance (101.12 mAh·g⁻¹ at 20 A·g⁻¹), and outstanding cycling stability with 89.18% capacity retention after 10,000 cycles. Notably, the cathode exhibits a thermodynamically favorable redox potential that allows spontaneous chemical oxidation by atmospheric oxygen, leading to an efficient self-charging function. The battery achieves an open-circuit voltage of 1.25 V and recovers 95.2% of its capacity without any external power input. This work offers a high-performance bipolar cathode design and a feasible strategy for building self-sustaining energy storage systems.