The typical way to do this is to read the password info from a configuration file. If your configuration file is called foobar.config, then you would commit a file called foobar.config.example to the repository, containing sample data. To run your program, you would create a local (not tracked) file called foobar.config with your real password data.
To filter out your existing password from previous commits, see the GitHub help page on Removing sensitive data.