Bob, your plan sounds workable only if you keep to an 1860's lifestyle. For instance, hand pump the water for washing you and your dogs, heat it on the stove, carry it to the bathroom and wash. Don't forget that washing and shaving was done in a small bowl with water from a pitcher and other duties were handled in the outhouse. Baths were taken in the kitchen to save on carrying the hot water and usually were in a big tin or copper tub.
This will serve to greatly limit the amount of water in the bathroom that can get on the floor. While today's finishes will go a long way to protect the wood, water will still be able to get between the planks, damaging it and whatever is underneath it. Eventually, the joists will rot and sag or break, leading to a major rebuild.
My 2 cents is that you should move up to about 1890 and put in linoleum. I doubt that you can find much that is still made of cork and linseed oil, but you should be able to find a style that will fit the era.
I'll bet that the original use of your room was not for a bath. It is possible in a few houses of the well-to-do, but this would be rare.