cement-boardcorner-beaddrywallshowertile
I need to finish the outside corner above the shower alcove. The shower ceiling is hardibacker and the wall outside the shower is drywall. Where these two meet, what is the proper way to finish it so it's a nice corner? I will just end up painting it.
The walls were easier because I had tile wrapping around the corner so I just taped and thinset those and tiled overtop. Not sure what to do for the ceiling since there won't be any tile.
A usual method is to go down the edge of the wall with a surface bullnose, showing a "knife edge" at the corner. This means the tile rolls down to meet the corner.
Another method, if your bullnose has finished bottoms, is to overlap the edge and go "around the corner", having the bullnose round into the outside wall (the wall that has the striped wallpaper) The bullnose will hide the tile edge, putting that grout line facing the side of the entrance.
This photo shows both methods: the left with a flat-on-wall knife edge and the right shows a wrap-around-the corner
You can use the edge profile pictured, in place of surface bullnose. You would adjust your tile to end short of the corner (equal to the edge thickness of the profile.
In all cases, grout would be filled into the corner/wall junction.
Joe, sorry to use the "answer" function again instead of adding another comment, I wanted to attach more pictures.
The tile I used was not available with a bullnose so I finished it flat on the sidewall. The edge cant be seen normally so I did not spend time making it perfect, but for your situation I retract my note about never finishing an edge with caulking. If you end flat to the wall around that corner it would be perfectly fine to use caulking for aesthetic purposes, use paintable caulk so you can paint a straight line down the whole side when you paint the wall.
Sorry I misunderstood your question, my situation was similar to yours and wrapping the tile around to the outside seemed like the best solution for me, and it looks pretty good that way (at least my wife did not complain, that's all that really matters). 
Best Answer
I had a similar situation where the backer board extended a few inches past my planned tiling edge in my shower. After I had finished with the tile, I taped the joint and applied joint compound over the backer board and it seems great. It's been three years and there is no cracking or any problem with it. That's not exactly an answer but I hope it helps you decide.