When an HC-05 Bluetooth module receives data via wireless does it write it to receive(rx) pin or transmit(tx) pin?
By a convention, Tx is the transmitting line (outgoing), Rx is the receiving one (incoming). So when two devices are interconnected the Tx of the transmitting device should be connected to Rx of the receiving device.

Update:
 To make it clear, decouple the HC-05 to the wireless part and to the wired serial. The statement above is true for the serial part. So, whatever is received wirelessly, is transmitted serially. And vice-versa.