Transient chaos and fractal basin boundaries are two important features of nonlinear multistable dynamical systems. Although their differences have been widely recognized, the intrinsic relationship between the dynamical complexity of transient chaos and the geometric complexity of basin boundaries remains unclear. Taking the bistable magnetic pendulum as a model system, we investigate this relationship through experiment, modeling, and numerical simulation. We first demonstrate experimentally the properties of transient chaotic motion and bistability in the magnetic pendulum. We then construct a simplified dynamical model and analyze the equilibrium points and their stability. Numerical simulations are performed to study how the basin structure depends on key system parameters, including the damping coefficient and the vertical distance between the pendulum bob and the permanent magnets. The transient sensitivity of trajectories is quantified by the finite-time Lyapunov exponent, while the geometric complexity of basin boundaries is characterized by the box-counting dimension. Our results show that, within the parameter range studied, stronger transient chaos is accompanied by more complex basin boundaries and a larger fractal dimension. In particular, the finite-time Lyapunov exponent and the fractal dimension of basin boundaries exhibit a positive correlation. This correlation can be physically understood from the local instability near saddle points and the associated escape dynamics in the multistable energy landscape. These findings suggest an intrinsic connection between trajectory-level dynamical complexity and basin-boundary geometric complexity in multistable systems, and may provide useful insight into transient behavior, sensitivity to initial conditions, and basin-structure control in complex nonlinear systems.