Update Jekyll local

I try to update my local Jekyll version on my machine and in my projects.

First i run gem update jekyll in iTerm to update Jekyll. This works. But how do I update the version in my project? Is there any command for the command line or should I change the new version only in my gemfile? When I run bundle update jekyll it only updates the dependencies in my gemfile.lock but not to the new jekyll version.

Thanks!