Well, here's what happened., and I know that I'm going to get yelled at.....
I left the mouse in with Ginger all night. I looked in before I went to bed, and the mouse was sleeping in one hide, and Ginger was asleep in the other one. I planned on returning the mouse to the pet store in the morning (I'm too sensitive to kill it myself). When I woke up and checked this morning, no mouse! A nice bulge in Ginger's tummy, and no mouse. I can only assume that at some point, Ginger realized the mouse was supper, and down the hatch it went.