@jonathanUE If you copy the SSL certificate from the old server to the new one and ensure your Web server (Apache) is updated, you shouldn't find any issues after changing the DNS settings.
For minimizing the downtime, the backup/restore process to another machine is the fastest due to not requiring any configuration, so in your case it would be the better option.
If you need to upgrade components in the Bitnami WordPress stack then backup/restore the entire stack is not valid for you, and migration would be the best choice (export WP data, content and configuration to another installation). In this case the downtime can be significantly higher if you're not experienced.