Problem to upload sketch trough bluetooth.

I have problem to upload this sketch to Arduino Uno trough bluetooth. I have tried both 57600 and 115200 baud rate.

#include   
int bluetoothTx = 0;  // TX-O pin of bluetooth mate, Arduino D2
int bluetoothRx = 1;  // RX-I pin of bluetooth mate, Arduino D3

SoftwareSerial bluetooth(bluetoothTx, bluetoothRx);
int led = 13;
void setup() {
  Serial.begin(9600);  // Begin the serial monitor at 9600bps
  bluetooth.begin(57600);
  pinMode(led, OUTPUT);

}

void loop() {
 digitalWrite(led, HIGH);
 delay(1000);
 digitalWrite(led, LOW);
 delay(1000);
}

I'm using following bluetooth module, SparkFun Bluetooth Modem - BlueSMiRF Silver. It seems to connect but after a while following error message appears and the connection is lost.

Arduino: 1.8.13 (Windows 10), Board: "Arduino Uno"

avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 2 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 3 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 4 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 5 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 6 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 7 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 8 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 9 of 10: not in sync: resp=0x28
avrdude: stk500_recv(): programmer is not responding

avrdude: stk500_getsync() attempt 10 of 10: not in sync: resp=0x28

avrdude done.

Can someone help me with this problem?

The 328P needs a reset to start the boot loader; I have my doubs that you can get that out of your bluetooth module. So when the upload starts, your only option is to press the reset button.

Note

Based on your sketch (and not on the comments in the sketch), your bluetooth is connected to hardware serial (pins 0 and 1). Why would you use software serial on a hardware serial port?