Your google approach was correct: http://drupal.org/node/529866 has a good rundown on this.
I asked about this at #drupal-support, and am waiting for an answer, but when I Googled it (+unserialize +"Error at offset" +"bootstrap.inc") I received 220,000 postings, so maybe this is a big issue I missed? Unserialize error at offset x of y bytes in boostrap.inc?