With the increasing incentives to improve public transportation service, as a means for addressing the current climate crisis, sociologists and urban planners, alike, have stressed the importance of improving transit service for all. This entails ensuring that vulnerable demographics are not neglected as urban planning shifts towards more sustainable modes. Research in transport justice reveals the concentration of economically vulnerable individuals in the urban core, granting better access to transit service due to the abundance of urban resources. However, these same works also point to the exclusionary effect that transit systems have on the lower-income individuals that reside in the periphery, while also highlighting how constraints on the neighbourhoods that public transit serves, can limit individuals' residential options. In this work, we develop a framework, using open-source data and tools, to explore the trends of socioeconomic transit inequalities with regards to neighbourhood characteristics. Specifically, for 9 cities in the USA, we define neighbourhoods based on their built environment (BE) characteristics. Then, we assess general transit characteristics across the BE groups, revealing better transit service for BE groups with higher density, diversity, and design. We incorporate socioeconomic characteristics of each neighbourhood, revealing how overlooking BE characteristics can obscure socioeconomic disparities in transit service. Finally, we compare our empirical findings to a null model that strips away the socioeconomic structure across neighbourhoods, showing the constraints that transit systems impose on residential locations. Ultimately, this work aims to motivate approaching transport poverty from a built environment perspective, to develop a more nuanced understanding of how transit service can be improved and how transit disparities in accessibility may impact individuals' day-to-day experiences.