I've found bitbucket authentication somewhat surprising and have described some of the interactions between private vs. public repositories and ssh vs. https URLs in JENKINS-24368. Unfortunately, all those investigations confirmed that I don't know how to access a private https based bitbucket git repository from the git plugin with either username / password or public key.
I can access a public https bitbucket git repository with username/password credentials.
I can access a private ssh bitbucket git repository with public key credentials.