Switch Input to Arduino Serial to Arduino Serial Output Led High or Low.

is there A faster way to send the serial data

Sure. Get out of the stone age.

  Serial.begin(9600);

should be

  Serial.begin(115200);

You need to read up on switch handling. Right now, as long as the switch is pressed, or released, you are hammering the serial port with data. You need to send a value only when the switch transitions from pressed to released and when it transitions from released to pressed. To do this:

int currState;
int prevState = HIGH;

void loop()
{
   currState = digitalRead(buttonPin);
   if(currState != prevState)
   {
      // A transition occurred...
      if(currState == HIGH)
         Serial.print('1');
      else
         Serial.print('0');
   }
   prevState = currState;

   // Other code
}