I want to programmatically trigger a backup in an IBM Compose database. Is there a REST API available for that?
From within Bluemix, no - there is no API available. Compose is looking to make the traditional Compose UI available from within Bluemix over the course of the next few months, at which time it will be. The documentation for the API can be found here: https://apidocs.compose.com/ (linked from https://help.compose.io)