Well “With Administrator Privileges” won’t require a password if you are running it as root, but if you’re not, i can see the problem there. If you wanted to enter the password before hand like you said, you could do something like this:
do shell script "stuff" user name "root" password "the_password"
of course the only problem there would be that the password would have to be in plain text, so you would have to make sure no one else gets ahold of the script. Also, you’d have to attach the “user name” “password” part to every shell script.