Thank you!   I thought I needed a script include for a business rule as well (like I said, still new at this!).   But this worked!   I had to change the values a little bit to:

var gr = new GlideRecord('u_assignment_record');

  gr.initialize();

  gr.u_number = current.sys_id;

  gr.u_assigned_from = previous.assigned_to;

  gr.u_assigned_to = current.assigned_to;

  gr.u_assigned_by = gs.getUserID();

  gr.insert();

And I removed the second condition, since I do want to track if someone change the value to nothing, but other than that, it works perfectly!

Can you just answer one more question for me?   Just to make sure I understand...the reason I don't need a script include from a business rule is because it runs server side already, correct?   Would there be any reason I would ever call a script include from a business rule at all (in a different case, not this one)?