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

Do you have the HC05 paired with the PC's Bluetooth? You may not be able to see it on a COM port unless it is first paired. This is between the HC05 and the PC. No Python involved yet.

I assume that when Python opens the COM port, with serialArduino = serial.Serial('COM4', 9600)it is the same as "connecting" with the Microsoft Bluetooth terminal app. The fast blinking light on the HC05 should then change to the blink every two seocnds. As Nick Pyner says, it the Bluetooth COM port is not not likely to be COM4.