Your screen is irrelevant. The default game resolution you specify in the game tab is what the base resolution will be for the game. The engine then scales the game up or down to each individual users display resolution & will automatically add black bars horizontally or vertically if needed as the engine keeps proportion when scaling.
My recommendation for if you want to actually work at 1080p is to buy a cheap 23" or 24" monitor which has a native resolution of 1080p. I work on my secondary hd monitor but often test on my laptop as I don't like constantly toggling between my laptop screen & secondary monitor as the primary display device as it often messes up my desktop icons!
P.S: the engine is not really adding black bars as such. It's the background color of the player window. The engine doesn't stretch the game backgrounds / images to fit the entire screen resolution as that would just look weird.