Start by not using SoftwareSerial on pins 0 and 1 if you're using an Uno, Nano, ProMini or Mega. Pins 0 and 1 are the HardwareSerial pins used for communication with the PC.
If you're using another board or a Mega, don't use SoftwareSerial.
try the SoftwareSeial library with pins 2 and 3 for TX and RX. Also write the same values to your Serial monitor so you can seen whats being send. And pins 0 and 1 are already your TX and RX so the software serial wouldn't be usefull with what you are doing now.
What shield? Is it not possible to make the connections over different pins?
And what Arduino boad?
I know how shields work, just seems odd to force use of pins 0 and 1, what are normally left unused for anything but loading code and the serial monitor.
Comment all reference to Serial and just use BTSerial and it should work.
Your problem is you have 2 jumpers at the lower section of the shield labeled tx and rx. The labels are on the underside of the board so you would need to remove the shield to see them. Serial is conflicting with BTSerial.
Those jumpers need to be moved to 2 and 3 in order for you to use
BTSerial.begin(9600); // Software Serial
Serial.begin(9600); // Hardware Serial to the monitor
in the same sketch.
Someone needs to verify what I say above. I can't determine where TX1 and RX1 is connected on the shield from the schematic. They don't appear to connect to pins 2 and 3
2 jumpers allow to select D0 and D1 or
D2 and D3 as serial communication port.
No other mention of the alleged jumpers and no picture. My assumption is that it must be documented on the board and obvious once someone points it out.
From examining the attached schematic, it doesn't appear that pins 2 & 3 of the jumper header (RX1 and TX1) are connected to anything. Verify continuity from these header pins to the Arduino header.
Keep in mind the above line will light the Uno LED, not the shield LED. The shield LED will flash when the BLE module it transmitting or receiving data.
Let's Back Up:
Follow the example on page 4 & 5. Make sure the power switch is OFF when you upload the code. Put the jumpers back in their original location and power switch ON after a successful upload.