Problem Definition
Currently there's no way to retrieve a list of build results associated with a label via a REST API. You can use the below API and filter for label:
https://bamboo/rest/api/latest/result.json?label=release
However, as per the documentation – it only works for top level plans. It does not include plan branch results.
The below Bamboo UI does show all results per label (even branches):
Suggested Solution
Improve the REST endpoint https://bamboo/rest/api/latest/result.json?label=release to allow retrieval of plan branch results too.