With the ever-increasing energy need to process big data, the realization of low-power computing technologies, such as superconducting logic and memories, has become a pressing issue. Developing fast and nonvolatile superconducting memory elements, however, remains a challenge. Superconductor-ferromagnet hybrid devices offer a promising solution, as they combine ultrafast manipulation of spins with dissipationless readout. Here, we present a type of nonvolatile Josephson junction memory that utilizes the bistable magnetic texture of a single mesoscopic ferromagnet. We use micromagnetic simulations to design an ellipse-shaped planar junction structured from a Co/Nb bilayer. The ellipse can be prepared as uniformly magnetized or as a pair of vortices at zero applied field. The two states yield considerably different critical currents, enabling reliable electrical readout of the element. We describe the mechanism that controls the critical current by applying numerical calculations to quantify the local stray field from the ferromagnet, which shifts the superconducting interference pattern. Our approach presents a route towards realizing superconducting memory applications by combining micromagnetic modeling with bistable spin-textured junctions.