I usually copy the variables/utils to my project (often just the variables)... when updating minor/point version updates, it's usually a quick diff against the framework version to see what's been added/changed. Major versions are usually close to a rewrite of the rendering templates/components, so that's the case regardless.

I have my own bootstrap.scss, with my own variables/utils... the rest point to the framework versions... It's pretty easy to do and works out really well imho. Of course, I often only change a few colors, and tweak some of the font defaults.