Re: argh bnet!
You can never trust b.net to hold a solo player game for you. Many say 5-10 minutes in a game will perm it long enough to allow you to go in and out (with no one else in the game), but I would never trust that theory. Even games that you are playing with others sometimes drop all players in the game.
I hate to say this, but it is less risky than the above scenario. I use this tactic a lot. Use a normal difficulty character to scan the Join games. Highlight a game name you think will have lowbies in it for awhile, such as "act 1ing", with your mouse and hit control + c on your keyboard. Get your muling character to enter the game with control + v, pasting the game name into the join screen. This will keep the game name in memory in case you forget it, and allow your character to get the items to join quickly after muling is dropped. Avoid games that say Perm, Perming, Mule Park, etc. because some people sit in these games with low characters waiting for someone to come in to mule. They will wait for you to leave and then max out the game with other characters, so you can't get back in, and they will search for your items. Or, they will simply hunt for your items faster than you can get back to retrieve. This has happened to me countless times.
Other options exist such as joining games that say "wait for free" or making a game called "Help Transfer" but these are as safe as the above scenarios.
The safest thing to do is to have a friend help you transfer in a private game.