You will need to it yourself. In this link below you can the general instructions.
There are two methods for this:
Migrate your current data to a new site with version 7.8 (preferred because all the components/server will be also updated). Basically you will just need to create a backup of the bitnami_drupal database and restore it in the new instance.
Upgrade your current version.
For the second method you need to follow the Drupal instructions for upgrading your site taking into account that the drupal installation directory is /opt/bitnami/apps/drupal/htdocs. That is substitions your current drupal version with the new one. You should have access to that folder using the bitnami user. You will need to keep the sites/default/settings.php from your current installation (don't overwrite it!).
Don't forget to create a backup before start migrating your data with any of the two methods.