You can't have two drivers (e.g. the BT TX and the other device's TX) driving the same input (e.g. the arduino's RX). At best, you get garbage; at worst, you damage something.
-j
Thanks for answering.
For now I fortunately don't need the other device's TX to transmit data to the Arduino's RX, so that won't be a problem for now - but later on... 
I'm aware that putting two TX's on the Arduino's RX is simply just begging for trouble, but couldn't an 74-something XOR solve the problem? Eg. that the TX from the device feeds into the XOR along with the RX from the Arduino. Thus, if data is currently being transmitted back and forth between the BT modem and the Arduino on the RX pin, the other device won't be able to "write" data to the pin - because of the XOR. The XOR would have to drive a transistor, so that it doesn't put logical 0 on the RX when it's idling.
Hmm... There might be some issues with feedback there. It's a bit messy (and only off the top of my head, I admit. I won't venture into that right now. :o