The strategic incorporation of beneficial nonlinearities has significantly advanced energy harvesting technologies; however, substantial efforts are expected for exploring the simultaneous application of bistable and quasi-zero stiffness mechanisms for ocean energy conversion. This study introduces a novel bistable electromagnetic wave energy converter featuring a bio-inspired X-shaped support structure and a mechanical-motion-rectifier (MMR). It represents the first integration of bistable and quasi-zero stiffness characteristics throughout the full operational range, enabling enhanced wave energy capture. The X-shaped structure accommodates large vibration amplitudes and offers tunable nonlinear stiffness properties, while the MMR—equipped with an energy storage and release mechanism—efficiently transforms linear motion into rotary motion, thereby amplifying instantaneous voltage and power output. Experimental results demonstrate that under wave conditions of 0.15 m height and a 4 s period, the system achieves a voltage peak of approximately 15 V and a power peak near 1 W. Compared to conventional linear converters, this design yields significantly higher power output, particularly at low frequencies, due to its bistable and quasi-zero stiffness features. These findings highlight the potential of the proposed nonlinear X-structured system as a floating-point energy converter for powering coastal monitoring stations and wireless communication devices in intelligent maritime environments.