Updated 12/1/15: add btrfs completions from debian.org

Updated 18/6/15: update toolbox/Fedora package manager commands from yum to dnf, remove defunct btrfs completions

It's easy really, use toolbox to install then copy the files into the host:

$ toolbox dnf -y install bash-completion wget \
  && toolbox wget https://raw.githubusercontent.com/docker/docker/master/contrib/completion/bash/docker -O /usr/share/bash-completion/completions/docker \
  && toolbox cp /usr/share/bash-completion /media/root/var/ -R  \
  && source /var/bash-completion/bash_completion 

Then, assuming your .bashrc is still symlinked to ../../usr/share/skel/.bashrc, dereference it and copy it over the link:

$ cp $(readlink .bashrc) .bashrc.new && mv .bashrc.new .bashrc

Then add bash completion to the resulting file:

$ echo "source /var/bash-completion/bash_completion" >> ~/.bashrc

Now BASH completion will be loaded into your shell when it starts.