If my corporation files for bankruptcy, does that mean we're out of business?

This depends on the type of bankruptcy filing. If you file for a Chapter 7 bankruptcy, your assets will be liquidated and it is highly unlikely you will have anything left to run your business. If you file a Chapter 11 or Chapter 13, you will be the Debtor in Possession and run your business while your creditors will be repaid under terms set forth by the bankruptcy court.