Exporting serial data from Arduino in real time

Yes. This is achieved by connecting Bluetooth to hardware serial pins 0,1, and no libraries are required, hence the code is exactly the same as that used to send the data to the serial monitor via USB cable.

You don't say which Arduino you are using but note that the port on pin 0,1 is usually shared with the serial monitor. This means that, if you do this:
1 you can observe two way serial traffic on the monitor
2 you cannot send from the PC
3. Bluetooth must be disconnected while you are uploading your programme.