Concerns over women's safety on public transport systems are commonly reported in the media. In this paper we develop statistical models to test for gender differences in the perception of safety and satisfaction on urban metros and buses using large-scale unique customer satisfaction data for 28 world cities over the period 2009 to 2018. Results indicate a significant gender gap in the perception of safety, with women being 10\% more likely than men to feel unsafe in metros (6% for buses). This gender gap is larger for safety than for overall satisfaction (3% in metros and 2.5% in buses), which is consistent with safety being one dimension of overall satisfaction. Results are stable across specifications and robust to inclusion of city-level and time controls. We find heterogeneous responses by sociodemographic characteristics. Data indicates 45% of women feel secure in trains and metro stations (respectively 55% in buses). Thus the gender gap encompasses more differences in transport perception between men and women rather than an intrinsic network fear. Additional models test for the influence of metro characteristics on perceived safety levels and find that that more acts of violence, larger carriages, and emptier vehicles decrease women's feeling of safety.