Hi! This is my first contribution and i hope it's not a repost, cause this bug has been around for a very long while.
What you want to do, is getting on top of the AH door from the inside. This is best done by flying inside and making a 180 degree corner straight away. This is the part that may take some practice to get right. As a warlock, i could also just use the double demon leap bug to get up there. If done correctly, you'll end up like this:
Next, toggle slow walking and walk off the border of the door till you end up here:
Now you want to jump to the wall, through the right window. Here's a screenshot with the direction:
When done right, you'll go through the window and fall through the wall. This will look something like this:
Now just step under the AH! From here on, you can mount up in the back part of the AH and continue your exploration trip. Have fun!