serial is print twice?
Probably the first time because you received the character '1' or '0'.
The second character is probably a '\0' or '\d', an end-of-string or end-of-line character.

You can easily check this by printing the value of each received character, like 

Serial.println((int)(BluetoothData));


You probably see the value for '0' (48), '1' (49), end of string '0' of end of line '13' or maybe '10' (new line).