This depends on how closely your designer's ideas can be mapped to existing Bootstrap components. If it's a very conceptual project (maybe an infographic or product advertisement) it may be better to start from scratch.
Most of the time though, I try to limit the extent of my designer's vocabulary by having them use a sketch template and see how far they get. There are iOS, Android, and even a Bootstrap template that they can start with: https://www.sketchappsources.com/free-source/349-bootstrap-3...
All of those usually resolve into components that can be mapped to something in Bootstrap or Foundation. If your designer can't solve an interface problem with something from those templates, that's often a sign that there's a bigger problem in your app's structure.
