Thanks. And there is no delay when you use the Pi?
If there is no delay when using the Pi, it’s caused by the operating system (which one) on the PC and I doubt you can do much about it.
If there is also a delay when using the Pi instead of the PC, there is a chance that it’s your Arduino code.
Lastly have you tried taking the Bluetooth out of the equation by using a USB connection for the serial communication? Do you have a dedicated TTL-to-USB adapter? Or do you have a second Arduino that you can use as a TTL-to-USB adapter? You can hook that up to the Arduino and test.
I have no idea which example that would be? Arduino example? Processing example?