You do not want to run a script as root, if it is not necessary. Never.
Instead you should run it as the user of this site.
Version 1:
$ sudo -i -u websiteuser
$ drush site-install ...
Version 2:
$ sudo -u websiteuser drush site-install ...
For version 1 the websiteuser needs to habe a valid login shell, because you login as this user and work in his shell session. You stay in websiteuser's login shell, until you explicitly logout.
For version 2 the drush command is run instead of the login shell. After the drush command, you are back in root shell.