Yeas, as others pointed out, the project file contains the MIDI data, settings, and pointers to the audio data files. So if you move it to another computer it cannot find the data files it's looking for.
A bun file stashes the audio data in the file as well. With file compression (Monkey's Audio or WinZip) you'll get a smaller file but it's still probably going to be prohibitively big for emailing (or for uploading somewhere for downloading if both of you don't have broadband connections to the internet.
Here's an approach I just started trying and it should work for pretty much any software.
Save the MIDI tracks (if any) as a SMF (standard MIDI file). Export the audio tracks individually as MP3s. I tried the 96kbps setting and each track is very close to the original and is a little less than 1MB per minute. At these sizes you might be able to successfully email the audio files individually, depending on whether your service provider's mail server has a file size limit.
On the other end, you get the files, open the MIDI file, save it as a project, import the audio tracks (if you exported from zero to the end they should line up perfectly).