Is your PC able to discover your Bluetooth module, and if so, what COM port does it use?
Until you get a UART functioning correctly again I wouldn't necessarily rule out the UART (it could be the hardware, the programming, the PCs configuration, the connection to the PC, etc).
I would try eliminating Bluetooth and try your code using a wired UART connection. If it works successfully, your problem lies in your Bluetooth implementation. If it doesn't work then I would try a different program, something simple like a printf() to the UART.
Once you get UART functioning with your program, I would then look at the Bluetooth module's datasheet again to see how its interfaced (it may require some form of initialization or have other special considerations that may have been overlooked).