Bruma was released on July 1st (PT), 2017 for the legendary and vanilla versions of Skyrim (PC). The Skyrim Special Edition version was released roughly two weeks later, on July 15th, PT. An XBox One edition is planned to be released sometime later.
Bruma is the only content-release of Beyond Skyrim: Cyrodiil for the Xbox, vanilla, and legendary versions of Skyrim. All future content from Beyond Skyrim: Cyrodiil will only be released for Skyrim Special Edition.
After Bruma's initial release, there have been several updates to account for bug reports.