Hi,
I don't know whether it may be part of your problem, you didn't tell how you connected the module, nor what sketches you've used.
Two things though.
You can't connect the module to pins 0 and 1 (serial-port) of your arduino-boards since they're already used to communicate with your PC. You will need the softwareserial or NewSoftSerial library to create a second port on other pins.
Second thing, when using serial ports, it's important to connect tx with an rx pin. Connecting tx with an tx pin and rx with an rx-pin doesn't work.
arduino <---> HC-05 module.
tx <---> rx
rx <---> tx
gnd <---> gnd