Wasn't aware that this could happen with BB as it doesn't dial as such. Do you still have your old dial up modem connected to both the PC and the phone line? If so pull the plug from the PC and only reconnect if BB goes down. Check for the presence of a dialler using something like Spybot.
If no modem still connected, makes me wonder if someone can hihack your phone line and spoof the call as coming from you?