One of our girls had this same problem when she's out for floor time and always gets her bottom all gross. A butt bath would probably be the easiest way to go about it. I know there's cat/dog bath wipes but I don't think they are safe for the piggies, there's some piggie safe shampoo that's fairly easy to find but we just use unscented baby shampoo as its already on hand for us. I have a small rubbermaid container (one a bit bigger than a shoe box) that's our designated piggie bath tub. And it's not a huge worry on them getting to cold if it's just a butt bath it will dry much faster than her whole body. Just try to soak as much of the water off as you can and maybe keep her wrapped in a towel for a few minutes to make sure she's only a tad damp. We use a small space heater in the room w the cage on bath days just because im a bit paranoid about drafts and feel it keeps the air a bit dryer. Hope it all goes well with your innaugural bath! Sometimes The girls can be a bit squirmy and fussy than the boys, in our house anyway!
