Behave Pro for Jira Cloud
GitHub Cloud and Bitbucket Cloud are both supported in Jira Cloud. On-premise versions of GitHub and Bitbucket are not supported in Jira Cloud.
Behave Pro for Jira Server and Data Center version 2.0+
The beta of Behave Pro 2.0 will support just Bitbucket Server and Data center. Currently Bitbucket Cloud, Github Cloud, and Github Enterprise (on-premise) are not supported in Jira Server or Data Center editions.
Behave Pro for Jira Server and Data Center version < 2.0
Git integration support will be introduced into version 2.0+ of Behave Pro for Jira Server and Data Center. Versions before this won't integrate with Git repositories tools at all. It is recommend to upgrade to version 2.0 when it is released.
What about GitLab?
GitLab support is in development for Jira Cloud, Server and Data Center. Further details