The tutorial on creating a Bootstrap 3 Skin (
http://www.dnncreative.com/Tutorial...ault.aspx) might be a good place to start, at least to orient you.
Basically, you want to alter what is displayed on the smaller screens. To do this, you can use media queries to apply special CSS to turn off display of unwanted content. If you want to do this only on the login page, it might make sense to use a custom login page with a special skin that simplifies this process. Add IDs or classes to make it easy to target those items that you want to disappear.