SHOOFILE  Birthday Bar does, indeed, connect to the internet periodically for two reasons:

First: the software will check to see if a new version is available by hitting shoofile.com once per week.

Second: the software will check the various amazon.com properties and present the user with an opportunity to go directly to that contact's wish list.

Each of these features can be turned off in the preferences by deselecting "Check for Birthday Bar updates" and "Check for Wish Lists" respectively.

I will update the documentation to address this issue in the next version.  
(Version 0.9)