I have created a tkinter GUI for my python script. When I run the script, I want a dynamic string in one of the Label widgets on the GUI window, which will display:
"Working."
Then:
"Working.."
then
"Working..."
and then start from "Working." again until the script is completed.
(Actually I'd prefer a progress bar in this area)
Is it possible?
Yes, it is possible. There are two ways to do it:

Whenever you want to update the label from your code you can call the_widget.configure(the_text). This will change the text of the label.
You can create an instance of a tkinter.StringVar, and assign it to the textvariable attribute of a label. Whenever you change the value of the variable (via the_variable.set(the_text), the label will automatically update.

Note that for either of these to work, the event loop needs to be able to process events (ie: you won't see anything if your function takes a long time to run and you never call update_idletasks or re-enter the event loop).
Python: Is it possible to create an tkinter label which has a dynamic string when a function is running in background?