We study buses' accessibility to education, health, and job opportunities in Santiago, Chile. Our approach computes travel times during a week using full real-world GPS data for the 6681 buses of the public transport system. The use of such disaggregated data allows us to calculate accessibility based on real operating conditions rather than planned schedules, as most previous contributions do. To develop our analysis, we divide the city into 1390 walkable zones, and we compute travel times between them. Then, we calculate the number of opportunities reachable from each zone to the rest of the zones, and we aggregate them at a municipality level. Our main finding is that public transport is not able to alleviate the inequality given by the geographical distribution of opportunities in the city. We also find that accessibility for public opportunities is quite more homogenous throughout the city compared to private opportunities. The center and north-east part of the city, where the wealthier municipalities locate, attain the highest levels of accessibility to jobs and private health institutions. The west part of the city shows worrying poor accessibility to complex hospitals, while the south part is excluded from job opportunities. Overall, policies should aim to mitigate these inequalities by improving the quality of public transport services. Conventional alternatives include increasing bus service frequency and expanding the dedicated infrastructure for public transport. In the long term, better city planning is required to facilitate spreading the opportunities all over the city.