Have you tried sending to yourself? A possibility that exists with all web-hosted email accounts is that the appropriate security settings, such as DKIM and SPF, may not be properly configured, causing the email to be rejected. If messages to yourself are not being received, I encourage you to contact Bluehost tech support to investigate.

I have only been sending to myself using a different email address as the recipient. The bluehost online webmail works perfectly, so I assumed it was not their settings that needed adjusting. From my perspective, only Thunderbird is having an issue, so I assumed it must be a setting in Thunderbird that needs attention.

Was that a wrong assumption?

Thank you for the suggestion though. I will follow up with Bluehost in the meantime to see if they have any insight as well.

Webmail does not use the same setup configuration. If you send from yourself to yourself and the mail doesn't appear, bluehost is rejecting it. If there was a configuration problem, bluehost would not have accepted the message for sending.