Your diagram shows your Bluetooth module connected to pins 0 and 1. Those pins are used for communication with the Serial Monitor through the USB cable.
I suggest you use SoftwareSerial to create another serial port on two other pins for your Bluetooth module.
And AFAIK you should connect Tx to Rx and Rx to Tx.
Are you sure your Bluetooth module can work with 5v - many can only take 3.3v?
...R