Since the outbreak of the 2019 novel coronavirus (COVID-19) pandemic, governments have been implementing containment measures aimed at mitigating the spread of the virus, including restrictions to human mobility. The ability to adapt to the pandemic and respond to containment measures can be bound by socioeconomic conditions, which are heterogeneous in large urban areas of low-income and middle-income countries. In this paper, we analyse mobility changes following the implementation of containment measures in Bogotá, Colombia. We characterise the mobility network before and during the pandemic and analyse its evolution and changes between January and July 2020. We observe a general reduction in mobility trends, but the overall connectivity between different areas of the city remains after the lockdown, reflecting the resilience of the mobility network. Then, we estimate a gravity model to assess the effect of socioeconomic conditions on mobility flows. We find that the responses to lockdown policies depend on the socioeconomic conditions of the population. Before the pandemic, the population with better socioeconomic conditions shows higher mobility flows. Since the lockdown, mobility presents a general decrease, but the population with worse socioeconomic conditions shows lower reductions in mobility flows. We conclude by deriving policy implications.