Is there even data to export? It appears to me the OP would need the bit.ly domain to preserve the links, otherwise he could just scrape all the URLs and find a way to redirect them.
They are (correct me if I'm not understanding how this service works) the only ones in a position to know which short URLs are already used and which ones are not.
So, if the list of short codes is short enough that he can search it in a couple of days and follow all of the links, then that's obviously what he should be doing rather than having public gripe time on HN.
(Then again, if he pays them just once he gets a decent bit of extra time, and they get paid for providing the service when his business was too small to justify him bringing his own infrastructure. Win-win?)