If you send just AT or AT+UART? do you get expected reply?
I think the device defaults to slave mode, could you emulate slave-loop mode within the arduino.
The documentation says you can only change baud rate in AT mode but later on has this...
If you want two Bluetooth Bee work together. One of it must be set as Master and the
other one be Slave.The 2 modules must have same pair number(default :1234) and Baud
Step1:Set one Bluetooth Bee as Master
Turn on AT switch and then power on the module to entering AT mode and send AT
that implies you can change other than the baud rate. Confusing to say the least.
Maybe someone else has a similar module and they can confirm what's true.