The rapid growth of Speech Emotion Recognition (SER) has diverse global applications, from improving human-computer interactions to aiding mental health diagnostics. However, SER models might contain social bias toward gender, leading to unfair outcomes. This study analyzes gender bias in SER models trained with Self-Supervised Learning (SSL) at scale, exploring factors influencing it. SSL-based SER models are chosen for their cutting-edge performance. Our research pioneering research gender bias in SER from both upstream model and data perspectives. Our findings reveal that females exhibit slightly higher overall SER performance than males. Modified CPC and XLS-R, two well-known SSL models, notably exhibit significant bias. Moreover, models trained with Mandarin datasets display a pronounced bias toward valence. Lastly, we find that gender-wise emotion distribution differences in training data significantly affect gender bias, while upstream model representation has a limited impact.