Magnetorheological dampers (MRD) are widely used in vibration control due to their rapid response and adjustable damping forces. However, conventional MRD designs with closed rectangular magnetic circuits suffer from limited effective working lengths and inadequate damping force for vehicle suspensions. To address this, a novel full-channel effective MRD with shunt and bending magnetic circuit (FEMRD_SB) is proposed. This design increases the effective working length of the damping channel by incorporating a bending motion in the magnetic circuit. Magnetic circuit shunting is integrated to mitigate magnetic leakage during bending, improving energy utilization efficiency. To better meet the practical needs of vehicle suspension, a quasi-static mathematical model aiming to explain the mechanical properties of the damper is investigated. Traditional models often overlook the uneven distribution of magnetic fields, which leads to poor modeling accuracy. To improve the precision of the quasi-static model, a multiphysical field coupling quasi-static modeling method is proposed. This method, utilizing the Takagi–Sugeno fuzzy neural network establishes the relationship between magnetic field and displacement, facilitating the integration of magnetic, flow, and solid fields for more precise modeling outcomes. Simulations and experiments validate the effectiveness of the FEMRD_SB and the quasi-static model. The real-vehicle experiments demonstrate that the FEMRD_SB effectively suppresses the sprung mass acceleration of a vehicle, improving the vehicle’s ride comfort.