The lived experience of urban life is shaped by personal mobility through dynamic relationships and resources, marked not only by access and opportunity, but also inequality and segregation. The recent availability of fine-grained mobility data and context attributes ranging from venue type to demographic mixture offer researchers a deeper understanding of experienced inequalities at scale, and pose many new questions. Here we review emerging uses of urban mobility behaviour data, and propose an analytic framework to represent mobility patterns as a temporal bipartite network between people and places. As this network reconfigures over time, analysts can track experienced inequality along three critical dimensions: social mixing with others from specific demographic backgrounds, access to different types of facilities, and spontaneous adaptation to unexpected events, such as epidemics, conflicts or disasters. This framework traces the dynamic, lived experiences of urban inequality and complements prior work on static inequalities experience at home and work.