In response to the issue of local damage to mountainous bridges easily caused by rockfall impacts, carbon fiber cloth and steel plate strengthening methods were adopted to deeply study the impact of the width of carbon fiber cloth and steel plates on the strengthening effect. This study investigates the strengthening effectiveness of Carbon Fiber-Reinforced Polymer (CFRP) wraps and steel jackets on circular bridge piers, utilizing the ABAQUS finite element method. The analysis focuses on the effects of varying load conditions and confinement widths ranging from 100 to 200 cm, with a specific case study of a bridge pier in Nanchuan District, Chongqing. The research results show that the width of carbon fiber cloth and steel plates has a significant impact on the bridge pier’s impact resistance and damage resistance. There exists an optimal strengthening width that maximizes the strengthening effect. The stress distribution and displacement changes under different load conditions are affected by the width of the steel plate; the wider the steel plate, the better the strengthening effect, but the effect is not strictly linear. A comprehensive analysis method integrating multi-directional stress and displacement data was developed, incorporating weighting factors based on structural safety relevance. For both strengthening methods, a set of fitted formulas for widths between 100 cm and 200 cm was derived. This study provides systematic insights and practical guidance for the design of impact-resistant strengthening systems for bridge piers.