They can swim, but they can't get OUT of the bucket, so they basically swim to death in the water.
Oh. Geez, I'd hate to run afoul of some of y'all.
I like Tom King's method. I've used it unintentionally, when I put some rubbermaid tubs on the back porch without their lids. I set them free in my field, so they can be coyote, fox and raptor chow as nature intended.
OP - as someone earlier said, you need to close off any entry points - and this may not be as easy as it sounds... I had a mouse problem in my old house - heard them in the walls, in the attic, etc. I hired an exterminator guy, who went around the place on the outside, using a mirror under some of the siding, and other sleuth type methods to identify 19 openings, including one where the mouse was actually watching! Those were closed up and he then undertook a process of killing them off in the attic. I dont know how he did that, and really didn't care. My neighbor down the street called same guy a few months later - she had over 30 openings in a smaller house than mine. CALL SOMEONE and get it done once and correctly. It wasn't that expensive.
We don't get less brave; we get a bigger sense of self-preservation........