Fe-Cr alloys are essential materials for core reactor components. The long-term in-core service of these components under intense radiation, thermal, and stress coupling conditions may potentially expedite the degradation of their mechanical properties. Radiation defects and insoluble helium gas molecules are generally trapped in voids or grain boundaries, forming intra- or intergranular fission gas bubbles. These bubbles cause irreversible radiation volumetric swelling and brittleness. However, a comprehensive understanding of the bubble formation process, particularly the effects of Cr content and dislocation stress field on the formation, remains unclear. As a mesoscale simulation approach, the phase field model coupled with irradiation, temperature, and elastic stress has been employed to study bubble evolution influenced by alloy composition and dislocation configuration. This approach offers advantages when addressing bubble-formation-related issues on different spatial and temporal scales. In this work, the phase field method is employed to investigate bubble growth kinetics and the effects of Cr content and dislocation stress field on bubble formation and evolution in Fe-Cr alloy under radiation. The simulations reveal that in an oversaturated gas and vacancy system, gas atoms tend to cluster at heterogeneous nucleation sites, such as vacancy clusters and dislocations, and grow by absorbing vacancy and gas atoms. The bubbles maintain a constant gas concentration up to a certain size as they continue to grow by absorbing vacancies. However, when the vacancy saturation is high, a bubble will behave as a void if its outward pressure is lower than the equilibrium pressure of a bubble of the same size. Cr additives reduce the diffusion rate of gas atoms and vacancies, extending the nucleation period of bubbles and decelerating their growth and coarsening. Dislocations cause vacancies and gaseous atoms to aggregate in the tension stress regions of the edge dislocation, enhancing the bubble's preferential heterogeneous nucleation in that area. This work discusses key kinetic elements affecting bubble evolution, including intrinsic microstructures and diffusivity. Further, it provides inspiration for future material designs for improving irradiation resistance and long-term service stability.