Welcome to the forums.
I hope I understood your question correct. You "installed" to an USB-drive using Unetbootin. And you don't notice any password present.
First off, Unetbootin does not install the OS, it only creates a medium (flashdrive) you can use to do a real install. A Bodhi Linux live-session by default has an empty password. This means you leave the box to fill in your password open when a program asks for it, you just hit Enter.
Installing Bodhi Linux to a drive, USB or HDD equally, is done by starting the live-session and use the launcher for the installer, either the icon on the left of the shelf, or the icon in the menu > applications. This will open a window with several steps to follow ending with a dialog to put in your name, the computer name and the username. Next you can provide a password. Username and password you should not forget as you will need those when running the installed system.
Let us know if this was the answer you needed or if you need to know more. By the way, most of the basic stuff a beginning Bodhi-user needs to know is explained in the quick start guide that shows when you boot the live-session, really worth reading.
CharlesGo to the full post