I decided to leave it be, although it couldn't get out of the tub. I draped the bathroom rug over the side of the tub, to give it a ladder to climb, then watched to ensure he was safe. He disappeared. I returned to my work.
Then one of the cats came in. And killed the mouse, presenting his body for inspection. Now I feel horrible. I didn't prevent the mouse's death by putting it outside, away from bloodthirsty cats. I know cats naturally prey on mice (and rats, which I am not fond of). And birds, although that's always very dicey, birds being so much larger than mice. One of the cats brought in a robin (a robin!) the other week who was severely mangled before being returned to the wild of the backyard. I have no idea if the robin survived.
The mouse certainly didn't. I should have put him outside. Poor wee mouse. Another life gone.
Lesson learned. The hard way.