The only real way to get rid of mice is to mouse-proof by blocking the holes through which they enter. You can kill a mouse or twenty, but if there is access, chances are that they’ll come back. You don’t want to keep killing mice; you want to find their path and block them out. If you are up one night at the usual time (and they do tend to have patterns of times they come and paths they follow), try to see if you can find the point of entry. Steel wool is effective for blocking. And you really don’t want them in your kitchen – nothing like mouse droppings in the pantry near your breakfast cereal to make you lose your appetite.
The problem with poison is if the mouse dies in the wall after ingesting the poison, that gets pretty smelly. For this particular mouse, though, if you know that the mouse passes through your bedroom door, couldn’t you just line the threshold with sticky traps?