In the event that you are denied employment by a private employer because of a bankruptcy you likely will not have rights against that employer.
The bankruptcy code does address current and prospective employment discrimination against someone that files for bankruptcy. The code places a higher burden on government agencies from using a previous bankruptcy filing as a reason for denying employment. Courts have interpreted the bankruptcy code to say that private employers are not held to the same rigorous standard and may deny employment upon learning that an applicant has filed for bankruptcy.
Employers are very savvy today. Do not hide the fact that you filed as it is likely they will find out about it anyway. There likely is a very good reason you filed. Divorce, a car accident, medical bills or unemployment are all good reasons why you filed and certainly will reveal that you are not an employment risk.