The presence of bias in data may affect the performance of deep neural networks, impacting their generality and accuracy on unseen data not presenting bias spurious correlations. In such scenarios, models are likely to learn shortcuts corresponding to bias rather than semantic attributes. To address this issue, assuming no prior information on bias is available, we propose a two-step method where an auxiliary model is trained with a selective gradient back-propagation strategy to provide bias pseudo-labels, later employed within a modified group robustness framework, optimizing worst-case subpopulation performance. Exploiting popular real-world datasets, we show how our method is effective in mitigating model bias dependency and improving generalization while outperforming available state-of-the-art methods.