In my day job, I work for an agency.

We get a design proof, in PSD format. I mentally translate it into a wireframe (which admittedly is kind of backward), and lay out that wireframe using the bootstrap classes that most closely match the layout. From there, I iterate, to match the design proofs.

The designers don't use any bootstrap design, so the bootstrap styles never come through in the final product.

The "right way" to do it (which I don't do) would be to use LESS mixins, so as not to have Bootstrap classes polluting the source, but I mostly work on short-turnaround projects so I stick with the Bootstrap classes.