You cannot use the serial monitor when you have the HC05 connected to hardware serial (pins 0 and 1). Only one device can be connected to a port at a time. Set up a software serial port to talk to the HC05 and then you can use the hardware serial and serial monitor to see what the HC05 sends. There is a software serial library that comes with the IDE. Easy to use but not as good as NeoSoftSerial or AltSoftSerial.
Connecting the HC05 RX directly to the Uno TX is risking damaging the HC05 RX input. Better to use a voltage divider to bring the Uno 5V TX signal down to 3.3V for the HC05.
Here is a quick test code showing how to use software serial. Mind that pin 4 on the Uno goes to the HC05 TX and pin 7 on the Uno goes to HC05 RX through a voltage divider (1K TX to HC05 RX, 2.2K HC05 RX to ground).
#include <SoftwareSerial.h>
SoftwareSerial mySerial(4, 7); // RX, TX
void setup()
{
// Open serial communications and wait for port to open:
Serial.begin(9600);
mySerial.begin(9600);
mySerial.println("Hello, world?"); // send to BT
}
void loop()
{ // run over and over
if (mySerial.available())
{
Serial.print(char(mySerial.read()));
}
if (Serial.available())
{
mySerial.write(Serial.read());
}
}