SpamHero is an excellent solution for customers at BlueHost that want premium spam filtering.  To ensure that no messages are bounced while activating SpamHero with BlueHost, it is very important that you set your Email Routing to use Local Mail Exchanger.  Otherwise, when cPanel sees that you've pointed your MX records to SpamHero, it incorrectly assumes it should tell your mail server to no longer accept email for your domain.

To change the Email Routing to Local Mail Exchanger in the BlueHost cPanel, start first by logging in.

Once you are logged in, choose the domains > zone editor option:

Scroll down to the MX (Mail Exchanger) section, and click the more >> button:

Once the page expands, choose the Local Mail Exchanger option, then click change:

Confirm that this setting is correct after you have setup your MX records to point to SpamHero.  If this setting is incorrect, you will see the following error in the delivery logs, and mail will bounce back to the sender:

550-Please turn on SMTP Authentication in your mail client.