Keyboard support is provided by the underlying GNU/Linux Operating System. We base GParted Live on the Debian SID GNU/Linux operating system.
In order to determine if this issue is a problem with GParted Live or a problem with upstream Debian SID it would help greatly if you can try booting Debian Live on your computer to see if your bluetooth keyboard is supported.
If it is supported on Debian SID, then we have a bug in GParted Live and we can start looking there.
If it is not supported on Debian SID, the it would help to create an upstream bug report so you could work with the Debian team on a resolution.
If you are in a rush then the short term solution is to try a different keyboard.