After a valid login with your current approach, encrypt the password using any of your algorithms or use the System.Cryptography class in .Net, store it in a place of the application feasilibility.
If you are sure that the user who uses your application has administrator priveleges, then look at Registry. If not look at storing the password in a flat file in the user's application data folder. You can access it thru the following snippet:
Environment.GetFolderPath(Environment.SpecialFolder.ApplicationData)
Again, encryption is your choice. Storing the password in the user's application data folder gives you certain security already.
So after your form loads, and the user enters the "username" , on tab out of the textbox, you need to call a function that would return the saved password from the registry/ flat file.
And then leave it to the user to control the flow.