The solution is to install Bower and NodeJS on Ubuntu 12.04 using the PPA provided by Chris Lea:
sudo add-apt-repository ppa:chris-lea/node.js sudo apt-get update sudo apt-get -y install nodejs
When this has installed, check the version:
npm --version 1.4.3
Now install Bower:
sudo npm install -g bower
This will fetch and install Bower globally.