Subjective bias is ubiquitous on news sites, social media, and knowledge resources like Wikipedia. Many existing methods for subjective bias correction have typically focused on making one-word edits and have been trained over a single (often, noisy) domain. In contrast, we propose a novel reinforced sequence training approach for robust subjective bias correction. Three of the unique characteristics of the approach are: (i) it balances bias neutralization with fluency and semantics preservation through reinforcement learning, to broaden the scope to bias beyond a single word; (ii) it is cross-trained over multiple sources of bias to be more robust to new styles of biased writing that are not seen in the training data for a single domain; and (iii) it is used to fine-tune a large pre-trained transformer model to yield state-of-the-art performance in bias text correction task. Extensive experiments show that the proposed approach results in significant improvements in subjective bias correction versus alternatives.