How can I pass data in real time to my PC running a python script via Bluetooth?

Your biggest mistake is using big words like "implement bluetooth functionality". As far as Arduino is concerned, there is no functionality other than connecting the bluetooth module, in your case the shield. As I said before, if Arduino code works via cable, there is no need to change it. Same port, and Arduino neither knows nor cares what is connected to it..

The other end is a slightly different matter, PC's bluetooth will be on a different port than the cable. I'm sure Python is no more interested in the mode of transmission than Arduino is, it just needs to know which COM port to listen to in order to get the serial data. Change the COM port code as required.