How Small the Problem Really Is
A mouse's skull sets the only real limit on where she can go: if her head passes through a gap, her flexible body follows. That means the space under a door, the hole where a pipe enters a wall, the vent of a radiator and the gap behind a loose skirting board are all open roads.
Start by freezing the scene. Keep the household's cats and dogs out of the area entirely, close windows, and make sure nobody opens the room door wide and breezes through.
Mapping Her Night Routes With Flour
Mice travel at night along walls, behind furniture and through the protected run behind appliances. Dust a thin line of flour across the skirting routes, the door threshold and in front of any hole or gap you can see, then leave the room dark and undisturbed. By morning the prints will show which corner she is living behind and which route she takes to explore.
Pair the flour with listening. Sit in the dark for ten quiet minutes and you may hear the faint scratching of a mouse shredding paper for a nest inside a drawer, a box of stored tissues or the stuffing of an old cushion. Note her base without tearing it apart straight away — knowing where she sleeps tells you exactly where the trap belongs.
Setting a Trap That Catches a Mouse Gently
A mouse is light enough that many box traps barely register her, so the reliable home option is the bucket trap: a deep, smooth-sided bucket padded with soft bedding, a ramp of books or wood leading up the outside, and a light tilting lid or cardboard disc baited at its edge with a smear of a favourite soft food and a few seeds, so she steps out, tips in and lands softly where she cannot climb out.
Place the trap flush against the wall on her flour-marked route, not in open floor. Set a second one near her cage if the room allows. Check traps at bedtime, once in the night if you can, and at dawn.
What to Avoid While She Is Loose
Never use poison or glue boards anywhere in a home with a pet mouse loose: both kill slowly and indiscriminately, and poison also endangers the cat or dog who later finds the body. Avoid snap traps for the same reason, and ask everyone in the house to check washing machines, ovens and recliner chairs before using them until she is home.
A mouse run to exhaustion in a warm room, or cornered by a well-meaning hand, can bite, injure herself in a desperate squeeze through a sharper gap, or vanish into a wall void she was previously ignoring. Containment plus a trap on her own route outperforms a pursuit almost every time.
Rehoming Her and Closing the Gap for Good
Once caught, settle her back in her cage with water, food and her old bedding, and watch her breathing and movement for a day; a mouse who is hunched, squeaking or dragging a limb after her adventure needs a vet's advice. Then examine the cage forensically: mice escape through bar spacing at door panels that is wider than elsewhere, chewed plastic bases and lids displaced at one corner. A tank-style home with a fine, firmly clipped mesh lid removes most of those routes at once.
Finally, note that a mouse outdoors is nearly invisible, which is exactly why KinsLe's Lost Pet Alert System helps if she ever gets that far: it alerts nearby Circle of Love members to check sheds and garages, and lets a finder message you directly with a sighting.