Addressing bias in NLP-based solutions is crucial to promoting fairness, avoiding discrimination, building trust, upholding ethical standards, and ultimately improving their performance and reliability. On the topic of bias detection and mitigation in textual data, this work examines the effect of different bias detection models along with standard debiasing methods on the effectiveness of fake news and hate speech detection tasks. Extensive discussion of the results draws useful conclusions, highlighting the inherent difficulties in effectively managing bias.