How to determine baud rate of microchip peripheral at runtime?
I once had a similar problem with a microcontroller which didn't have a UART nor exactly known clock frequency (crystal was too expensive). 
I let the other party send a specific byte, for instance 0x01 and measured the time the bus was low. This was 8 bit times (startbit + 7 zeros of data). So dividing this by 8 I got the value I should set my timer to.
So, before you configure the I/O pins for UART use them as common I/O until the Bluetooth module sent this agreed upon character and time it. You could do this running a loop, or use timer capture to detect the falling and rising edges (more accurate).