Bankruptcy is a Public Record

Bankruptcy is a civil court filing in the Federal Bankruptcy Court.  Therefore, since the public is paying for the court and all of it's employees and filings, your bankruptcy petition filing is a public matter.  This does not mean that your name will be posted on a bulletin board at the courthouse or at work.  The public filing will be able to be found by the public if they do a www.google.com or www.yahoo.com search for your name.  Unless someone is looking for it, they will likely not find it.

Additionally, you are only required to make one appearance in a Chapter 7 Bankruptcy and one or two in a Chapter 13 bankruptcy, depending on your state.  In a Chapter 7 bankruptcy, if you hire a competent bankruptcy lawyer and with a little luck, you will never have to step foot in a courtroom.  Your only appearance will be at a Meeting of Creditors or a 341 Meeting.  In a Chapter 13 bankruptcy, depending on your state, you may or may not have to go to a confirmation hearing.  Your bankruptcy lawyer will be at both hearings with you and the hearings will not cause you much trouble. 

A Bankruptcy Filing is More Private Than You Might Think 

Unless you need to stop a garnishment or do an automatic withdrawal for a Chapter 13 bankruptcy payment, there is no reason for your employer to find our about a bankruptcy.  Unless you tell them, there is no reason for your friends or co-workers to find out about your bankruptcy.  Unless your friends or family are creditors, the court will not notify them in any way.  You are further protected from unethical debt collection practices by the Automatic Stay and the discharge further protects you from any creditor publicizing your bankruptcy.