Using the current version of git-client-plugin 1.15.0 and git-plugin 2.3.4 the cloning of a private bitbucket.org repository does not work.
It used to work with git-client-plugin 1.3.0 and git-plugin 1.5.0.

I created a new "Free Style" job, entering only a Git SCM with https://username:password@bitbucket.org/user/repository.git as "Repository URL" leaving everything else as default.
I'm aware of the credentials functionality, but I need to use https://username:password@bitbucket.org/user/repository.git URL syntax, for otherwise certain post build steps will not work.

This is the output I get:

Started by user Flavio Donzé
Building in workspace C:\data\jenkins\workspace\workspace\git_test
Cloning the remote Git repository
Cloning repository https://username:password@bitbucket.org/user/repository.git
> C:/Progra~2/Git/bin/git.exe init C:\data\jenkins\workspace\workspace\git_test # timeout=10
Fetching upstream changes from https://username@bitbucket.org/user/repository.git
> C:/Progra~2/Git/bin/git.exe --version # timeout=10
> C:/Progra~2/Git/bin/git.exe -c core.askpass=true fetch --tags --progress https://username@bitbucket.org/user/repository.git +refs/heads/:refs/remotes/origin/
ERROR: Error cloning remote repo 'origin'
ERROR: Error cloning remote repo 'origin'
Finished: FAILURE