Arduino Uno R3 hardware serial: peripheral interfering with the USB/Serial-converter?
Those two resistors, marked RN4A and RN4B, are used to protect the uart line from conflicts, while also assigning priority to the external header. They act like weak pullups, in that anything before (In this case, left of) the resistors will only affect the line after them, if the lines are not being used.

Anything serial connection plugged into the header, will take priority over the Arduino's usb/serial connection, as they can directly power the lines.

But this will also provide issues during programming, so use an enable pin, or power switch, or simply remove the bluetooth module while programming.