How can I delete a remote Git repository from the command line (Git Bash)?
As Jubobs mentioned above you can use github dev API, so:
curl -u :username -X "DELETE" https://api.github.com/repos/:username/:repo
Where :username = your username(github handler) and :repo = a name of a repo you want to get rid of
As pointed out by BrokenBinary in his comment,
This can't be done.
You cannot delete a remote repo (hosted on GitHub or elsewhere) with Git commands, be it in Git Bash or elsewhere, period. You can delete remote branches (assuming you have write access to them), yes, but not an entire remote repository.
However, the GitHub Developer API allows you to delete, from your shell, a repo hosted on GitHub.