I'm also on Bluehost, it looks like there have been some issues with other people using Bluehost. I don't know if you've had any new information on the problem. Here's how far I've gotten.
I configured WP Mail SMTP and the test emails are working fine. I am able to send the test emails successfully using both the 465 and the 26 ports through Bluehost's SMTP mail.johnevanofski.net . I have tried using both: Send all WordPress emails via SMTP and Use the PHP mail() function to send emails to no avail. :(
Your email form is the best on WordPress and I'd be so sad if I wasn't able to use it. Hopefully this is something you can fix, I'll totally go pro if you can. Thanks!