Program arduino via USB while using a Bluetooth module (HC-06)
The link in question was correct... you do need to unplug it.

The Arduino's serial chip uses pins 0 and 1 to communicate with the ATmega 328 PU chip onboard, thus you have two independent devices connected to the same wires and both the Arduino main chip and the Bluetooth module are trying to communicate at the same time (rendering all data unreadable by the computer).