When I moved my WordPress sites to a new server, I used the All-in-One WP Migration plugin:
https://wordpress.org/plugins/all-in-one-wp-migration/

If your site isn’t huge, it’s quite easy. If your Uploads directory is huge, you can migrate that part yourself and the plugin will handle the rest.

@jeez

If BlueHost provides SSH access which allows you tar your files, dump your databases, etc, then it’d be much easier, though most shared hosting providers don’t. Without SSH, you’re pretty much limited to moving things manually or using a plugin if your shared hosting environment will allow it to run.

I mention the last part as not all plugins account for environments that impose limitations on the time a process can run, and many shared environments place strict limits on RAM and CPU usage. If you’re in the process of moving a small site, that shouldn’t be an issue, but any site with a good amount of data may be an issue.

In addition to AIO WP Migration, Duplicator is also a pretty good plugin.

https://wordpress.org/plugins/duplicator/

There’s also BackupBuddy, though it’s commercial, thus not freely available. I can, however, say that it works very well. I’ve moved quite a few clients away from shared hosting using it.

https://ithemes.com/purchase/backupbuddy/

As far as the manual route, in the event the plugins fail, you’d need to use phpMyAdmin to backup the databases and then manually download and upload your files to the Droplet. You would then either install phpMyAdmin on the Droplet (if it’s not already) and import the databases, or use Adminer (which is what I recommend as it’s a single file and you can just delete it when you’re done).

https://www.adminer.org/#download