How to download/ save my own website?

You have a few options:

1. Use a WordPress backup plugin, like UpDraft to create a backup of your WordPress files and database. UpDraft and other plugins can create a file to download, or even put the backup in your Google Drive, DropBox, and other locations.
2. BlueHost is a cPanel based provider, which means you can do a full cPanel backup, which would backup everything. This would include websites, databases, and email. However, unless you are moving to another cPanel based provider in the future, this is more cumbersome, but still useful.
3. You can manually download your WordPress's document root and contents (likely public_html) via FTP, as well as export the database to a .sql file from the command line or MyPHP Admin and download it.

You should be able to talk to BlueHost's support and they should be able walk you through any of these steps (or just do it for you). Requesting backups for people leaving a hosting provider is standard procedure.

When it comes to Wordpress sites, on all the sites I've worked with (hundreds) there are 2 things that need to be backed up -

1. The Wordpress files and
2. The Database dump.

The easiest way is to log in to Wordpress as an administrator, install a plugin and back everything up with the plugin. I usually use Updraft (which breaks the files down into subcategories - you back them all up, as well as the database). Another common choice is Backup Buddy. No doubt there are others. The point being that you can do a full backup from within Wordpress - and this is likely the safest and easiest way.

If you want to go the harder route - The alternative way requires you to get the Wordpress files and the database dump off the server.

Start by grabbing the files. You may be able to do this through FTP or SCP or even through a drag-and-drop interface. The exact method of how you do this depends on what your hosting provider offers.

The database will almost certainly be MySQL, so you can use PHPMyAdmin (which is often a component of CPANEL, but can be stand-alone. If you have access to PHPMyAdmin but don't know the connection details these can be found in the file wp-config.php in the root install of your Wordpress site. Just open that file with a text editor and have a look for the lines which read "define(DB_?????.'xxxxx') where the ????? is the username, password, database name, database server, and the xxxxxx is the value. You will likely need the username and password to use PHPMyAdmin. (There are alternative ways of getting the database dump, but they are a lot harder)

Depends on what you want to save, and what you want to do in future.

BackUpWordPress has gotten me through 2 server moves, including one that involved rapid unplanned redeployment (my server hardware failed). It'll back up your database (and the site proper if certain prerequisites are met), and between that and backing up your wordpress directory, redeployment is fairly simple.

Wordpress also has an XML export/import option I'd recommend. Its probably easier, but untested.

I'd recommend doing both in case ;).

HTTrack and wget will back up static versions of your page. Its great if you never intend to blog any more but want to stick the files up for access or want a simple to deploy static copy of it somewhere. These options will be snapshots of your site in a point of time not a full wordpress backup for the future.

There's probably nothing worse than thinking you've backed up, then realising its just a snapshot of the site in time, and you can't get your site back up.

If there's anything super critical you want static snapshots of, and need access you might want to make sure those pages are spidered/cached on the internet archive or archive.is