There's a couple of things I would try.
First: Don't use the native Arduino TX/RX pins, they should be left alone to talk to the computer. Use SoftwareSerial instead in start a separate serial connection.
Second: Check that Arduino TX pin (that you declared in softwareSerial) is connected to the BC127 RX and vice versa. Unlike just about every other connection in electronics, serial connections need to have their pins reversed so that TX talks to RX. It's an easy mistake to make and one I've made when not paying attention to what I was doing.
Third: Flow control.
If the BC127 sends data when the Arduino isn't listening the data could be lost, to prevent this the BC127 won't send until the Arduino signals it is ready through flow control.
See the BC127 datasheet page 8, pins 40 and 43. Trying tying UART_CTS to 3V3 and UART_RTS to Ground. That should cause the BC127 to be in a constant 'send' state.
Lastly I'd hook up a couple of LEDs to pins 37 and 38. They should give you some sort of status indication that could be useful in debugging future problems.