In bipartite causal inference with interference, two distinct sets of units exist; interventional units, which receive treatment, and outcome units, where outcomes are measured. Which interventional units’ treatment can drive which outcome units’ outcomes is often depicted in a bipartite network. We study bipartite causal inference with interference from observational data across time and with a changing bipartite network. Under an exposure mapping framework, we define causal effects specific to each outcome unit, representing average contrasts of potential outcomes across time. We establish unconfoundedness of the exposure received by outcome units based on unconfoundedness assumptions on the interventional units’ treatment assignment and the random graph, hence respecting the bipartite structure of the problem. Harvesting the time component of our setting, causal effects are estimable while controlling only for temporal trends and time-varying confounders. Our results hold for binary, continuous, and multivariate exposure mappings. For binary exposure, we propose three matching algorithms to estimate the causal effect by matching exposed to unexposed time periods for the same outcome unit. We show that the bias of resulting estimators is bounded. We illustrate our approach through simulation studies and a study on the effect of wildfire smoke on transportation by bicycle.