Management of ecologically significant urban green space is likely to be increasingly governed by biodiversity policy frameworks. These frameworks tend to reproduce bounded thinking and strategies that separate green space from its context and characterise people as a disturbance. Like many green spaces these ecologically significant areas are highly valued by visitors and nearby residents. Green space is important for engagement with nature, social interaction, and for respite from daily life: it is strongly connected to surrounding areas and to the lives of people who live there. The dissonance between bounded management thinking and the role of green space in resident's lives may compromise conservation goals if boundedness remains a central concept in management. For an ecologically significant and heavily used area of bushland in suburban Australia we examine management frameworks and the relationships of visitors to the bushland. We find that visitors value the bushland for its social role and as a valuable remnant of native vegetation where they can experience a variety of associations with flora, fauna, and what they perceive as a relatively intact 'natural' landscape. Concepts central to management frameworks such as 'biodiversity' were not well understood but were incidental to visitors' understanding of the bushland as environmentally valuable and as an asset to the area. Current management frameworks fail to acknowledge these contemporary associations and isolate the bushland in time and space. We identify where official management frameworks and visitor associations with the bushland diverge and potentially converge and suggest alternative directions for management.