I tried working with Bootstrap 3 a few times last year, and while I liked the grid & responsive utility classes, everything else was just way too much. You can configure your Bootstrap build using their customizer to only include the grid, but for my needs I had to fork it (to make it work with LessPHP, without normalize.css, and because I needed to rename the xs, sm, lg class names). I uploaded the result to my github:
https://github.com/zirafa/bootstrap-grid-only
Generally I've avoided using grid systems for many years as the designs and projects I worked on never really warranted investing the time and effort when I could simply float a few blocks here and there. Especially for fluid responsive designs, the older non-responsive grid systems would just get in the way...
But working on a very large project with many people, and dealing with configurable responsive templates, a responsive grid becomes essential to keep things organized and to make quick changes. Thankfully the popularity of frameworks like Bootstrap and Foundation have also reached a critical mass where designers understand the grid and are designing more with a responsive grid in mind.
There are still some annoying problems (improper nesting can cause headaches), but the newer grids are definite time savers. I recommend pairing the Bootstrap-grid-only with cherry picked styles from Skeleton.css which I find to be much simpler than investing in the totality of the Bootstrap ecosystem.