If a game is more than 5 minutes old it will stick around for a bit even when the last player leaves.
Thus, if you only have 1 CD key:
- create a game with the mule
- stay in there for at least 5 minutes
- leave the game
- join with your playchar. If the game is still there, you know you've really waited long enough
- drop a few of the items you want to move. More if they aren't worth a lot, just one if they are insanely valuable
- leave game
- join with mule
- pickup item(s)
Repeat as needed.
However, there is now the "realm down" issue --- if you do things too fast bnet will lock you out, and you'll loose whatever you've dropped. It may work if you join with a different IP address, but only once (unless you change address again), but I wouldn't rely on that. Better work slow, so a realm down doesn't happen at all.
You can also do this during playing --- play as usual, drop the items you want to mule, join with the mule, join with playchar again, continue playing, drop items, ... If you're not sure whether you've been in the game long enough, just leave and join again to verify that the games sticks around.
WARNING: other than realm down, another trap is that games will also stick around for a short time if they are less than 1 minute old. I wouldn't recommend using that; better wait the 5 minutes.