Go to http://getbootstrap.com/customize/ and toggle just what you want from the BS3 framework and then click "Compile and Download" and you'll get the CSS and JS that you chose.
Open up the CSS and remove all but the grid. They include some normalize stuff too. And you'll need to adjust all the styles on your site to box-sizing: border-box - http://www.w3schools.com/cssref/css3_pr_box-sizing.asp
I would suggest using MDO's http://getpreboot.com/ instead. As of v2, preboot back ports the LESS mixins/variables used to create the Bootstrap 3.0 Grid System and is much more light weight than using the CSS generator. In fact, if you only include preboot.less there is NO overhead because the entire file is made up of mixins/variables and therefore are only used in pre-compilation and not the final output.
Checkout zirafa/bootstrap-grid-only. It contains only the bootstrap grid and responsive utilities that you need (no reset or anything), and simplifies the complexity of working directly with the LESS files.