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

I hooked up this program to two Arduino's. It works ok, but is there A faster way to send the serial data.
I have to hold down the switch, to make the led go on. I would like it more like Momentary Push Button switch (High when pushed, Low when off).

int LedPin = 13;
int buttonPin = 10; 
int TxPin = 0;
int RxPin = 1;

int buttonState = 0;

void setup ()
{
  Serial.begin(9600);
  pinMode (LedPin, OUTPUT);
  pinMode (buttonPin, INPUT);
  pinMode (TxPin, INPUT);
  pinMode (RxPin, OUTPUT);
}







void loop()
{ // Down here where it belongs
  buttonState = digitalRead(buttonPin);
  if (buttonState == HIGH)
  {  
    Serial.print('1');
     
  }
  else
  { 
    Serial.print('0');
  }
  
  
  
  
 int Rx = Serial.read() - '0';
  
  if (Rx == 1)
 {
  Serial.println("Led is on");
 digitalWrite(LedPin,HIGH);
   
 }
 
 else if (Rx == 0)
 {
 Serial.println("Led is off");
  digitalWrite(LedPin,LOW);
  
 }
 
 else
 {
   Serial.println("Invalid!");
 }
}