Hi Marjorie,
Thanks for posting this question on the forums. I’ve had my personal website hosted by Bluehost for several years, so I can hopefully point you in the right direction.
Omeka uses PDO, which provides a data-access abstraction layer packaged with PHP and enabled by default. We need this to make the necessary database connections, edits, and additions. For some reason, Bluehost has a policy of disabling PDO on all their servers by default, but is willing to change the setting for users who need this functionality. At this time, Omeka requires PDO to run smoothly.
It’s likely that you don’t PDO enabled already for your Bluehost account. To double check or make such a request, visit the Bluehost Helpdesk (http://helpdesk.bluehost.com/help) and open a ticket. Based upon my research, most if not all other shared hosts including Dreamhost keep PDO enabled; Bluehost remains an odd exception.
The parse error you’re experiencing in the core file is related to the PDO connection, so I’d start troubleshooting there. However, without PDO a message should appear that says "could not find driver," rather than giving a fatal error. Is it possible you also edited the core file by accident, or removed one of the necessary quotes from the db.ini file? There shouldn’t be a parsing error, and I can’t replicate it. If it persists, we’ll have to dig a little deeper.