Those instructions, although it mentions "private", are only valid for a Public repository, as you have noted without a similar style to the GitHub integration we don't have a way to setup a shared token you would need to be able to authenticate. That said today, you cannot really use a pull method to pull changes from BitBucket to DevOps Services, you will need to use a push method from somewhere that you can authenticate to your private repo and the DevOps Services git repo to keep them in sync.
https://developer.ibm.com/answers/questions/197619/continuous-delivery-with-bitbucket-and-jazzhub.html