In a previous series of posts, we had the chance to build a Really Minimal theme for WordPress 3.5 and higher. In case you missed those posts, you will find a link to them at the end of this article. I recommend you get yourself familiar with them before reading on.
As you recall, the theme we built was indeed minimal and it missed in particular any kind of styling. The recent release of Bootstrap 3.0 by Twitter gives us the chance to style our theme and, as a bonus, to turn it into a responsive design.