If I use this line to install a drupal site it only runs fine if the 'mydb' database already exist.
If the database doesn't exist I get an error. Is there other drush command to make an installation when the database doesn't exist?
drush si --db-url=mysql://root:root@localhost:8889/mydb
I don't think is a user permission since the root user has all privileges enabled. Look the picture. I use MAMP (the free version)
I this other capture you can see the connection parameters: