A significant level of stigma and inequality exists in mental healthcare, especially in under-served populations, which spreads through collected data. When not properly accounted for, machine learning (ML) models learned from data can reinforce the structural biases already present in society. Here, we present a systematic study of bias in ML models designed to predict depression in four different case studies covering different countries and populations. We find that standard ML approaches show regularly biased behaviors. However, we show that standard mitigation techniques, and our own post-hoc method, can be effective in reducing the level of unfair bias. We provide practical recommendations to develop ML models for depression risk prediction with increased fairness and trust in the real world. No single best ML model for depression prediction provides equality of outcomes. This emphasizes the importance of analyzing fairness during model selection and transparent reporting about the impact of debiasing interventions.