Electronic voting has a wide range of applications in modern society. Self-tallying voting, which allows all voters to calculate the results themselves, is gaining popularity as it eliminates the need for a centralized authority. However, existing self-tallying voting schemes face challenges, such as the lack of a score voting mechanism and inadequate privacy protection. To address these issues, we propose FP-BSS, a full privacy, blockchain-based self-tallying score voting protocol. We extend the traditional binary voting paradigm to support score voting, enabling voters to rate each candidate within a specified range. Candidates with broad acceptability tend to win, while extreme candidates favored by a minority but opposed by the majority are less likely to win. Simultaneously, to guarantee ballot privacy both during and after the election, we design a full privacy ballot encryption scheme leveraging blinding factors to ensure complete voter anonymity, and propose a new zero-knowledge proof to verify ballot legitimacy. We prove that FP-BSS achieves full voter privacy and meets all necessary security requirements. Performance results demonstrate that FP-BSS provides enhanced security while maintaining reasonable practicality.