As cities become increasingly developed, inclusive and equal provision of public services and affordable housing is essential in achieving sustainable growth and development. In Singapore, with much of the population living in public housing and taking public transport, there is a great need to understand their landscape across the country. In this study, using tools from Complexity Science, we elucidated the spatial organization of places in Singapore through public bus transport connectivity, and investigated the association between such pattern to the distribution of the population age groups and property price. From the spatial network of the public transport services, we probed the places’ scale using the continuum percolation approach to uncover their spatial pattern. After that, we employed an information-theoretic measure of complexity to quantify the spatial organization of the system. The results show that there is a critical distance embedded within the public transport system at which the structure of the places in Singapore emerges. In many areas, the connectivity between places map well, and are greatest within the official planning boundary, demonstrating the influence of upstream spatial planning in determining bus networks. Yet in mature towns (particularly those in the central region), bus connectivity spans beyond planning boundaries, suggesting a more organic pattern on the ground in places with a longer history of development. The complexity of the bus network maps remarkably well to residential areas, and was associated with the distribution of resident age groups, and to property prices. In particular, the well-connected areas in and around the central region of Singapore are associated with higher property price and an older population. In contrast, the peripheral less-connected areas tend to see a lower property price and a younger population. The findings can contribute to understanding the existing pattern of physical and social form within an urban system, highlighting the role of complexity science methods in uncovering ‘emergent’ patterns in bus transport networks, beyond initial spatial plans, as areas mature over time. It can also guide future planning by highlighting the areas where more attention is needed to enhance island wide public bus connectivity, and by doing so, enable the public transport system to contribute to reducing potential socio-economic polarization within the system.