A new Single-sided Variable Flux Permanent Magnet Linear Machine with flux bridge in mover core is proposed in this paper. The flux bridge prevents the leakage flux from the mover and converts it into flux linkage, which greatly influences the performance of the machine. First, a lumped parameter model is used to find the suitable coil combination and no-load flux linkage of the proposed machine, which greatly reduces the computational time and drive storage. Secondly, the proposed machine replaces the expensive rare earth permanent magnets with ferrite magnets and provides improved flux controlling capability under variable excitation currents. Multivariable geometric optimization is utilized to optimize the leading design parameters like split ratio, stator pole width, width and height of permanent magnet, flux bridge width, the width of mover’s tooth, and stator slot depth at constant electric and magnetic loading. The optimized design increases the flux linkage by 44.11%, average thrust force by 35%, thrust force density by 35.02%, minimizes ripples in thrust force by 23%, and detent force by 87.5%. Furthermore, the results obtained by 2D analysis are verified by 3D analysis. Thermal analysis is done to set the operating limit of the proposed machine.