Permissions to create a database with drush command? 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:
I don't think Drush has an option for this built into the site-install method but you might find something under the sql-sync method, which I think has an option to create a database.

I don't know if it's appropriate for your situation but you might want to look at the Drupal Quickstart: Pre-made Development environment; it has a bunch of custom Drush commands included, one of which will set up an entire site (vhost file, database, file permissions, etc.) in one line:

drush quickstart-create all --domain=example1.dev


I've copied this command out and hacked it to pieces, and now I can install a fully configured Drupal site on my local Mac machine with a single terminal line:

drush isosc --domain=example.dev


I would thoroughly recommend doing this; I couldn't live without it now