How do I delete a Git branch locally and remotely?

Question

Failed Attempts to Delete a Remote Branch:

$ git branch -d remotes/origin/bugfix
error: branch 'remotes/origin/bugfix' not found.

$ git branch -d origin/bugfix
error: branch 'origin/bugfix' not found.

$ git branch -rd origin/bugfix
Deleted remote branch origin/bugfix (was 2a14ef7).

$ git push
Everything up-to-date

$ git pull
From github.com:gituser/gitproject

* [new branch] bugfix -> origin/bugfix
Already up-to-date.

How do I properly delete the remotes/origin/bugfix branch both locally and remotely?