Bluetooth module HC-06 slow data throughput - Is it the baud rate

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Hello I am using the HC-06 UART Bluetooth model in serial port profile mode (default). I want to run this thing as fast as possible, so this must mean setting the baud rate. I do this in my Arduino program through an AT command, I have set in window's device manager so that the COM port operates at 115200, finally in my C# program to benchmark the speed I also set the baud rate to 115200.

var sp = new SerialPort("COM4", 115200, Parity.None, 8, StopBits.One);

My arduino program looks like

void setup() {
    Serial.begin(9600);
}
 
void loop() {

   char *buffer;
   String s;
   int i = 0;
//set baud to 115200
      Serial.print("AT+BAUD8");
//string of 100 chars
      s = "JnlJe1RsUCRid59ZoHBTIKk1KaBpeB35avPPYDRFgeyldvB5BBfR3F7iudjSq0XltRskENoTrIIKF93z9oKfh0lnfx3B76CdfQYs";   
   for( i = 0; i < 19; i++) {
//40 s
    Serial.print(s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s+s);
   }
    delay(1000);
}

However I'm currently only getting about 8000 bits per second (so I'm guessing the baud is at 9600 still?). What do people think?

Thanks
Thomas