With the large-scale development of unconventional oil and gas resources such as shale oil and shale gas, bridge plug perforation combined with fracturing has become the main technology for staged fracturing in horizontal wells. However, due to the influence of casing deformation and the promotion of techniques such as casing window sidetracking and casing patching, soluble bridge plugs are required to effectively seal the original casing while being able to smoothly pass through small-diameter well sections. Therefore, starting from the design of bridge plug structure, material selection, finite element analysis, etc., a small-size soluble bridge plug suitable for sudden changes in casing inner diameter is designed. Additionally, the stress mechanism of the bridge plug and tool string downhole is studied and analyzed, and a set of models for calculating the downhole motion and pumping capacity of small-size soluble bridge plugs and tool strings is established. The research indicates that the inclination angle has the greatest impact on pumping capacity, while the mass of the tool string has the least effect. The size of the annular gap between the bridge plug and casing, pumping speed, and pumping capacity are positively correlated, while the viscosity of the pumping fluid is negatively correlated with pumping capacity.