Is it possible to use Bento for Mac as the database for a database-backed website? I'm looking to create a website on my Mac, with content coming from a database also on the Mac. The website is static, and I'll probably need to write some scripts that will periodically (1) create new HTML pages on my Mac based on new content in the database, (2) sync the HTML pages on my Mac to the web server on the Internet using SFTP.

Can this be done using Bento, or should I be looking into Filemaker Pro instead?
Bento isn't well-suited for your needs, in my opinion. It's possible to export information from Bento into a variety of formats, including text files, Numbers, or Excel. But it doesn't have the hooks needed to be queried by a Website creation tool. As you mention, FileMaker Pro does have that ability. Here is their web publishing page.

This may be overkill for you, but if you're familiar with SQL databases, you might also take a look at Sequel Pro.