How was the backup created?. Ideally it should only be a SQL file and the public folder, right?. If so, you could follow this steps to deploy your backup as if it was a "custom php application": http://wiki.bitnami.com/Applications/BitNami_Custom_PHP_application
You will need to create a database in the MySQL server. To connect to it, you can follow these steps: http://wiki.bitnami.com/Components/MySQL#How_to_connect_to_the_MySQL_database.3f
With that, you will not face any compatibility problem with new Mediawiki.
If what you want is to use a new mediawiki version, you could try to import the SQL file that you have to the mediawiki database and try to follow the oficial database update procedure (keep in mind that you need to run the command inside the Bitnami Console and inside
If you need help on this approach, don't hesitate to ask us again and we will help you on this approach.