The syntax for adding a private package to a python requirements.txt is shown in the sample requirements.txt file. This assumes that the client that is installing the package has the proper permissions to access the file. In my case, using bitbucket pipelines, I can create an SSH key for the pipeline and add it as a read-only access key to my bitbucket repository.
It is typically:
git+ssh://git@bitbucket.org/<fork>/<reponame>.git
NOTE: the .git link does not include the colon after the domain name, it's instead a / character. Also, there is a
git@ user specified.