Bluetooth mouse and bluetooth receiver

I have a Precision M6300 that I bought and installed a bluetooth radio (transmitter receiver) for. I bought a bluetooth mouse to use (very expensive when you consider you can get mice for a couple bucks if you want a cord) and after some hunting in the software for the bluetooth got the mouse working. It worked well for 2 days when a fellow worker dropped the mouse on the floor. I bought an inexpensive mouse that said it was bluetooth but it had its own USB Xmitter/Receiver with it. It works well (except when the mouse decides to sleep and won't wake up unless you click a button, sound familiar Microsoft Mouse users?) but I wanted to use the Dell receiver I bought for the laptop, not this USB plug in. Does anyone know if bluetooth connection should work to any receiver as long as a encryption code is not used? I can pick up printers and cell phones and head phones when near by but not this new mouse.