Using su to become root without a password is the same as allowing root to log in without a password. It creates a big security risk.
But, for a script, I'm not sure why this is necessary. You can just run the script as root, or you can have the system run it as part of boot up or under cron.
As I read the command (not a script), you want to su to the user "bschorun", and then run the command "tmboot -y". You can su to become any user if you are root--or have root priveleges. But you can't su to another user from your login--unless you have the user's permission.
Perhaps you can describe more about what you are trying to do.