I think that in order to do this you'd probably need some kind of radio device connected to the computer, such as the SINCGARS radios used by the military.
You could also use a cell phone if you had one and send it that way, but I'm guessing that would be pretty easy to trace. And if I saw the cat actually hooking up a cell phone to my laptop even more red flags would start to go up.
As others have mentioned earlier you can connect to a wireless network with the right kind of card. However, in the year 2000 wireless networks weren't really all that prevalent yet, at least not like they are now. I seriously doubt the laptop was connected to a wireless network at the time. If the bus was in motion at the time (which isn't really clear in the story), I think it would pretty much have been impossible.
Why does anyone believe any part of the stories told by family and friends? Was there a bus? The only fact is that someone unsavory had Berg's password.