In case you have warning message about insecure user and password usage from command line you can do following:

1. use mysql_config_editor set login-path=local host=localhost user=db_user password executed in container via exec. That will create encrypted file.
2. Specify --login-path=local instead of -u user and -p password in your backup script.

I have my backups via rsnapshot. This is something like TimeMachine for Mac with handy directory structure and without duplication.

And my backup script looks like this:

/usr/bin/ssh -i /mnt/HD/HD_a2/ffp/home/root/id_rsa_nexus.key -C core@myipaddress "docker exec itservice_db_1 mysqldump --login-path=local itservice_production" >
 mysqlbackup.sql

That will create mysql dump on your remote backup host without passing user and password in more secure way.

docker-compose exec db mysql_config_editor set --login_path=local --host=localhost --user=itservice --password

will ask password and save credentials in container.

Resources: http://stackoverflow.com/questions/20751352/suppress-warning-messages-using-mysql-from-within-terminal-but-password-written